 1395 phycal.HLP, Generated by A3UTIL.EXE, 1994  (c) PCSCC Inc., 1993,01|┌!JÿDàεbö╢F|┌X▓▀ I]                                                                             ┌─────────────────────────┐                                             │╒════════════════════════╧╕                                            ││    Application File     ├─────────────────────────────────────       ││                         └──────────────────────────────────────      ││                                                                      ││            Interactive Problem Solving in                            ││                                                                      ││      PHYSICS, APPLIED PHYSICS AND PHYSICAL CHEMISTRY                 ││                                                                      ││             Using AstroFormulaCalculator 3                           ││                                                                      ││      Application File  Version 3.10a   09-01-1993                     │                                                                                        by  P. DuBois Murphy, Ph.D.                                                                                                    (c) Copyright 1981, 1993  PC SuperComputer Capital, Inc.                                                                                                            All rights reserved.                                                                                                     Read and understand  WARRANTY INFORMATION . Type J twice to read.                                                                            Instructions on using help file are at end of file. Type K to read.                                                                                                                                                   ╒══════════╕                                                            │ CONTENTS └──────────────────────────────────────────────────────────                                                                          0.00                  Table of Contents                                                                                                               *    To quickly jump to Sections, position the Section line number      *    on the │JUMP│ line (line 12) and type J or type Lxxx (enter)       *    where xxx is line number. For example, to jump to line 139,        *    type L139 (ent).  Type S or R to skip back/forth to Sections.                                                                         SECTION                   TITLE                              PAGE│LINE                                                                           0.00 ... Table of Contents ................................... 1   29  1.00 ... Introduction ........................................ 2   70  2.00 ... An Introduction to Calculations Using ............... 4  148           AstroFormCalc 3.                                               3.00 ... Vector Addition. .................................... 6  264  4.00 ... Acceleration, Velocity and Distance in a ............ 7  320           Straight Line.                                                 5.00 ... Uniformly Accelerated motion in Two Dimensions. ..... 9  385  6.00 ... Electromagnetic Radiation: The Blackbody ........... 11  490  7.00 ... Tension, Compression, Shear and Elasticity ......... 12  537  8.00 ... Circumference of an Ellipse: Calculation by ........ 14  606           Series and Integration                                         9.00 ... Ideal Gas Law Calculations. ........................ 15  656  10.0 ... Resistance and Capacitance. ........................ 15  690  11.0 ... Geometric Optics: Lenses and Mirrors ............... 17  767  12.0 ... Impedance and Radio Frequency Matching ............. 19  834  13.0 ... Useful Calculations for Problem Solving in ......... 20  888           Applied Physics.                                               14.0 ... Glossary of Terms .................................. 22  982  15.0 ... Product License and Warranty. ...................... 23 1045  16.0 ... Product Information and How to Order Complete ...... 25 1108           Package.                                                       17.0 ... Other Astro 3 Products ............................. 27 1198  18.0 ... Order/Registration Form ............................ 28 1243  19.0 ... Instructions for Manually Installing Package. ...... 29 1308  20.0 ... Interested in Becoming the Author of Your Own ...... 30 1349           Interactive Application File?                                  21.0 ... Help File: Summary of File Viewing Commands ........ 30 1369                                                                        ╒═══════════════╕                                                       │ INTRODUCTION  └──────────────────────────────────────────────────────                                                                         1.00          Introduction                                              ────────────────────────────────────────────────────────────────────────                                                                                 To change the display colors to high-intensity white on blue            type Q when the highlight bar is lighted on the EQU below.                                                                             'EQU                                                                    'COL HWHITE BLUE                                                        'HELP                                                                                                                                                    This document is an on-line application file which discusses            the theory and presents solved problems in Physics and related          subjects such as Material Science, Physical Chemistry and               Optics.  Excellent references, which can serve both as a                supplement to an existing course in Physics or as a stand-alone         study or self-help guides, are the books:                                                                                                                                                                                        "Applied Physics", 2nd ed.                                               Arthur Beiser, Ph.D.                                                    Schaum Outline of Theory and Problems                                   McGraw-Hill Book Company, New York                                      1988                                                                                                                                           "The Physics Problem Solver"                                             Dr. M. Foigel, Chief Editor                                             Research and Education Association                                      61 Ethel Road West, Piscataway, New Jersey, 08864                       Revised Printing 1992                                                                                                                          "Modern Physics"                                                         R. Gautreau, Ph.D. and W. Savin, Ph.D.                                  Schaum Outline of Theory and Problems                                   McGraw-Hill Book Company, New York                                      1978                                                                                                                                           "Physics for Engineering and Science"                                    D. A. Wells, Ph.D. and H. S. Slusher, D.Sc.,Ph.D.                       Schaum Outline of Theory and Problems                                   McGraw-Hill Book Company, New York                                      1983                                                                                                                                           "3000 Solved Problems in Physics"                                        Alvin Halpern, Ph.D.                                                    Schaum's Solved Problem Series                                          McGraw-Hill Book Company, New York                                      1983                                                                                                                                  Personal computers (PC's) and their automation and calculation          capabilities were not available before 1981.  Proper use of the         PC can reduce or eliminate much of the tedium associated with           reducing theory into algebraic expressions and then into useful         day-to-day applications.                                                                                                                        This PC application file is intended to provide students of             Physics with help in mastering the execution of the necessary           algebra and math calculations upon which Physics is heavily             based.  The application is driven by a versatile                        spreadsheet/calculator call AstroFormulaCalculator 3 which              exists as the file ACAL3.EXE.  This program is specifically             tailored for analysis based on algebraic expressions, formulas          or equations.  One of its main functions is to eliminate the            "programming-type overhead" in working with known formulas and          to allow meaningful learning to proceed rapidly.                                                                                                AstroFormCalc 3 can be used with any traditional outline manual         or text to develop equation templates that solve specific               problems.                                                                                                                                       This file is organized by topics with are summarized in the             Table of Contents.  The use of AstroFormCalc 3 is discussed in          the on-line help file which is accessed by typing (F1) from the         equations display.  This entire file can be searched using the          auto-search command "A".                                                                                                               ╒═══════════════════╕                                                   │ HOW TO CALCULATE  └───────────────────────────────────────────────────                                                                        2.00     An Introduction to Calculations Using AstroFormCalc 3.         ────────────────────────────────────────────────────────────────────────                                                                                 This Section provides an introduction to numbers, number                formats, variables, variable names, mathematical operations,            equations and related topics.  In general, in order to avoid            ambiguities, one must always express numbers, mathematical              expression and equations in an acceptable way when entering             them into a computer program.  These requirements lead to the           formulation of a set of rules which are summarized in the               on-line Help File for the ASTRO 3 program.  This help file can          be reached from the main equation display by typing the (F1)            key.                                                                                                                                            For example:  It is very common to have to evaluate an                  expression which might be written as:                                                                                                                                   456.789 x 0.345                                                                                                         As written, one would interpret this expression as:  Find the           product that results from multiplying the decimal 456.789 by            the decimal 0.345.  Because the letter symbols are most often           associated with variable names, the use of "x" as a                     mathematical operator for multiplication and the                        equally-acceptable use of "x" as a variable name in an equation         such as "y=x" would result in confusion for the                         expression-interpreter of the program.  As a result, the                multiplication operator is commonly the "*" symbol and the              "by-the-rules" way to enter the above expression would be               456.789 * 0.345 (enter) In the language of "computerese",               "(enter)" means to type the enter key of the keyboard and               usually results in some sort of computer action.                                                                                                The following examples illustrate some common ways to write             mathematical expressions and the "by-the-rules" way they are            entered into the ASTRO 3, and many other, computer programs.            These examples exist as equations templates that can be                 "called-up" by scrolling the screen until the highlighted bar           appears over the appropriate 'EQU line.                                                                                                         After the templates are loaded, follow the instructions and             always type (F2) from the main equation display to return to            this application helpfile immediately after the 'EQU reference.                                                                        Topic # 1: ENTERING NUMBERS and EXPRESSIONS                                                                                                     Discussion: The following examples show common representations for       expressions and the proper way to enter these into this program. These  expressions can be entered at the ENTER variable below.                                                                                            commonly used     ASTRO 3 way     Result          Reason                                                                                         24.1 x 56.7       24.1*56.7      1366.47        * means multipl.                                                                                     5                                                                       -            5/180          2.77E-2 or    / means division             180                          2.77*10^-2                                                                                                        6 ∙ 3 ∙ 4      6*3*4          72           * not ∙ for multipl.                                                                                 2(-7)5         2*-7*5         -70            implied multipl.                                                        not allowed.                                                                                       25÷5           25/5           5            / is division operat.                                                                                                                                                         2      5                                                             14 -  + 8 -  (14+2/7)+(8+5/9)   22.84           express compound           7      9                                     fractions as sums                                                                                                                                                                                                                                                                                                 'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSWRIT      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 2: ENTERING EXPONENTS and SQUARE ROOTS                                                                                                  Discussion: The following examples show common representations for       expressions and the proper way to enter these into this program. These  expressions can be entered at the ENTER variable below.                                                                                            commonly used     ASTRO 3 way     Result          Reason                    ___                                                                    √144         (space) sqr(144)  12         use sqr(..) function                                                    to take square root.           2.3                                                                   10             10^2.3           199.5       ^ means raise to power               4                                                              5.67 x 10      5.67e4            56700      e means base 10                 4     3                                                             3x10 -2x10     3e4-2e3 or        28000      calculation in                             3*10^4-2*10^3                scientific notation.            2 -1                                                               (2x10 )        (2e2)^-1          0.005    no implied exponentiation                                                                              ___                                                                    √ 6                                                                     ------    (space) sqr(6)/(4*sqr(3))   .3535  must match parentheses     4√3                                                                                                                                                                                                                                                                                                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSEXPO      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          The remainder of the on-line manual studies many scientific             concepts which when grouped together are commonly called                "Physics".                                                                                                                             ╒══════════╕                                                            │ VECTORS  └────────────────────────────────────────────────────────────                                                                        3.00       Vector Addition.                                             ────────────────────────────────────────────────────────────────────────                                                                                 Vectors are useful tools to understand the behavior of many             phenomenon.  the following discussions and problems deal with           vector addition                                                                                                                        Topic # 3: PERPENDICULAR VECTOR ADDITION, RESOLVING A VECTOR INTO        PERPENDICULAR COMPONENTS, TRIGONOMETRIC METHOD                                                                                                 Discussion:                                                                                                                                                                             * <- psi                                                              *  │                                                       resultant  *    │                                                          R     *      │ vector                                                       *        │  A                                                         *          │                                                theta  -> *____________│ <- 90 degrees                                             vector B                                                                                                                                                                                    Enter any two of three lengths of vectors, one must always be zero. R   and RESULTNT must be 0 or positive. If warning messages, lengths are    inappropriate.                                                                                                                                 'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSVECT      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 4: PERPENDICULAR VECTOR ADDITION                                                                                                        Problem # 4.1: An airplane is flying at 500 mi/h into a crosswind of     300 mi/h.                                                               (a) What is the planes airspeed relative to the ground?                 (b) In what direction should the plane head relative to its original    ground direction so as to maintain its original direction with respect  to the ground?                                                                                                                                 'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS2P3       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 5: PYTHAGOREAN THEOREM                                                                                                                  Problem # 5.1: If the hypotenuse, or long side, of a right triangle is   100 cm long and one of the short sides is 33 cm long,                   (a) what is the length of the other side?                                                                                                      'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS2P16      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒════════════════╕                                                      │ MOTION in LINE └──────────────────────────────────────────────────────                                                                        4.00       Acceleration, Velocity and Distance in a Straight Line.      ────────────────────────────────────────────────────────────────────────                                                                                 Discussion:  An object has an initial velocity VELINIT and is           accelerated at a constant rate ACCELER to average velocity              VELOAVE and travels DISTANCE in TIME.                                                                                                                                                                                        -------------     ACCELER                                               │  OBJECT   │     ---->       straight line                             │           │     VELOCITY    ----------->                              -------------     ---->                                                       | .......>.....>.......>.....|                                          0                           TIME                                                                                                     The following problems illustrate some relevant concepts.                                                                              Topic # 6: VELOCITY and ACCELERATION versus TIME in a STRAIGHT LINE                                                                             Problem # 6.1: While at an army base, a person observes the flash of an  M1-A1 tank's main gun and hears the sound 5.2 s later.                  (a) If sound has a velocity of 1095 ft/s in that region, how far away   is the tank?                                                                                                                                   'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS3P2       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 7: VELOCITY and ACCELERATION versus TIME in a STRAIGHT LINE                                                                             Problem # 7.1: A cheetah can reach a speed of 30 mi/hr starting from     rest in 10s.                                                            (a) What is its acceleration?                                           (b) how far has it gone in the 10 s?                                                                                                           'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS3P7       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 8: VELOCITY and ACCELERATION versus DISTANCE in a STRAIGHT LINE                                                                         Problem # 8.1: While parked on a steep hill, a car's emergency brake     fails and it accelerates at 16 ft/s^2 downhill.                         (a) How much time does the man, 100 ft downhill, have to get out of     its way?                                                                (b) At what velocity will it hit him?                                                                                                          'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS3P11      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 9: VELOCITY and ACCELERATION versus DISTANCE in a STRAIGHT LINE                                                                         Problem # 9.1: If A CD-10 jetplane needs at least a velocity of 200 m/s  to take off from a 1500 m runway.                                       (a) What must its acceleration be from rest and                         (b) how many seconds until takeoff at this acceleration?                                                                                       'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS3P12      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════════╕                                                       │ MOTION in 2D  └───────────────────────────────────────────────────────                                                                        5.00       Uniformly Accelerated motion in Two Dimensions.              ────────────────────────────────────────────────────────────────────────                                                                        Topic # 10: UNIFORM ACCELERATED MOTION in a VERTICAL PLANE                                                                                      Discussion: Falling bodies, near the earth, all have a uniform downward  acceleration from the earth's gravity, G=32 ft/s^2 or 9.8 m/s^2. A      uniform gravitation field G will result in VELOCITY at TIME and a       distance, or HEIGHT, for the free fall.                                                                                                                          start at rest, initial velocity=0                                                |   -----                                            G    │             V     │                                            gravity│             |   HEIGHT                                                V             V     │    <- VELOCITY at TIME                                        -----------                                                                                                                                                                                     Use these equations when velocity and time are important factors.       G=gravity, V=final velocity at time T, H=distance traveled at time T.   Enter value of gravity G and at least two other variables with nonzero  values.                                                                                                                                        'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSUNMO      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 11: UNIFORM ACCELERATED MOTION in a VERTICAL PLANE                                                                                      Problem # 11.1: A superball dropped from the rivergate bridge hits the   water in 3.95 s.                                                        (a) What is its final velocity in ft/s and                              (b) how high is the rivergate bridge above the river?                                                                                          'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS4P1       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 12: UNIFORM ACCELERATED MOTION in a VERTICAL PLANE                                                                                      Problem # 12.1: A construction worker drops a hammer from a roof gable   24 feet above the ground.                                               (a) How long does it take the hammer to reach the ground?               (b) What is its final velocity?                                                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS4P2       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 13: MOTION of PROJECTILES in UNIFORM GRAVITY                                                                                            Problem # 13.1: A football is thrown with a perfect spiral at an         initial velocity of 70 ft/s an at an angle of 40 degrees with respect   to the horizontal.                                                      (a) How far away should the receiver be.                                (b) How long will it take to arrive?                                                                                                           'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS4P9       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 A plot of the downfield height vs. time  of the football follows.                                                                                                                                                      32-                                c   c  c                               |                            c       ^     c                            |                        c      max height     c                        |                      c      31.6 at 1.45 s.    c                      |                    c                             c                  24-                  c                                 c                  |                c                                     c                |               c                                       c               |             c                                           c             |            c                                             c          16-           c                                               c           |         c                                                   c         |         c                                                   c         |       c                                                       c       |       c                                                       c     8.-     c                                                           c     |     c                                                           c     |   c                                                               c   |   c                                                               c   | c                                                                  c0.-c <Passer throws ball                         Receiver catches it > c  ||--------------|--------------|--------------|--------------|--------   0             .61            1.22           1.83           2.5                                 HEIGHT[c]  vs. TIME                                                                                                   To plot this file, load the equations below and follow the instructions.                                                                        Topic # 14: MOTION of PROJECTILES in UNIFORM GRAVITY                                                                                            Problem # 14.1: A football is thrown with a perfect spiral at an         initial velocity of 70 ft/s an at an angle of 40 degrees with respect   to the horizontal.                                                      (a) Plot the football's height vs. time.                                                                                                       'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS4P9P      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒════════════╕                                                          │ RADIATION  └─────────────────────────────────────────────────────────                                                                         6.00       Electromagnetic Radiation: The Blackbody                     ────────────────────────────────────────────────────────────────────────                                                                                 Electromagnetic radiation propagates through space in                   wavefronts of fluctuating magnetic and electric fields.  The            frequency of this radiation identifies it as radio waves,               microwaves, infrared, visible UV and so on.  The first equation         template identifies the kind of radiation from its frequency or         wavelength.                                                                                                                            Topic # 15: ELECTROMAGNETIC SPECTRUM, FREQUENCY, WAVELENGTH                                                                                     Problem # 15.1: Enter frequency in Hertz or wavelength in meters. One    or the other should be entered as 0.                                    (a) What radiation has a wavelength of 400 nm (400*10^-9 m)?            (b) What radiation has a frequency of 400 THz (400*10^14 Hz)?                                                                                  'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSSLWV      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          A blackbody is the "perfect" absorber of all incident                   electromagnetic radiation.  It is also the "perfect" radiator           because it is in equilibrium at a fixed temperature and so must         emit all its incident energy.  However, the wavelength                  distribution of its emitted radiation follows Planck's Law,             Setfan's Law and Wien's Law and is usually in the infrared              region, hence the term "blackbody".                                                                                                    Topic # 16: RADIATION, POWER EMITTED vs ABSORBED, STEFAN'S LAW,          BLACKBODY                                                                                                                                      Problem # 16.1: A household-type 'radiator' has an emissivity of 0.6 an  area of 2.0 m^2                                                         (a) At what rate is radiation absorbed by the radiator when the walls   of the room are at 27°C?                                                (b) At what rate is radiation emitted from the radiator when its        temperature is 50°C?                                                    (c) What is the net radiation rate from radiator?                                                                                              'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS1946      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════════╕                                                       │ STRESS/STRAIN └───────────────────────────────────────────────────────                                                                        7.00       Tension, Compression, Shear and Elasticity                   ────────────────────────────────────────────────────────────────────────                                                                        Topic # 17: TENSION, COMPRESSION, SHEAR, ELASTICITY AND YOUNG'S MODULUS                                                                         Discussion: Below the elastic limit, or maximum stress that can be       applied to an object without causing permanent deformation, a tension   or compressive force FORCE acts on an object of initial length LENGTH0  and cross-sectional area AREACROS to change its length by DELTALEN.     Young's modulus YOUNGMOD is the ratio: (longitudinal                    stress)/(longitudinal strain) and it has the dimensions of a stress     (N/m^2 or Pascal Pa and pound/in^2).                                                                                                                              ______________________   A=cross-sec area                              /____________________ /|                                               |       OBJECT        |A|  --->                                         |_____________________|/   FORCE                                                                                                                |---LENGTH0--------|--|                                                                    DELTA                                                                   LENGTH                                                                                                                                                                                                                                                                                                                              'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSYMOD      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 18: TENSION, COMPRESSION, SHEAR, ELASTICITY AND YOUNG'S MODULUS                                                                         Problem # 18.1: A 10 ft. 0.02 in^2 diameter copper wires is stretched 0. 10 in. by the force of a 200 lb lead weight.                            (a) Find the stress on the wire .                                       (b) Find the resulting strain.                                          (c) Find Young's modulus for the wire material.                                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS1302      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 19: FORCE, COMPRESSION and YOUNG's MODULUS                                                                                              Problem # 19.1: Agents are monitoring the weight of suspected            contraband in a warehouse by monitoring the length decrease of a 15 ft. strategic hollow steel jack which supports the floor.                   (a) If the jack's inner diameter is 2 in., outer diameter is 3 in.,     Young's modulus of the steel is 3.5*10^7 lb/in^2 and the tube length    decreased by .008 in, what is the weight (force) of contraband?                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS1305      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 20: ELASTIC LIMIT, TENSION and YOUNG'S MODULUS                                                                                          Problem # 20.1: A steel-like polyimide rod is 6 m long and 4 mm in       diameter. The elastic limit is a stress of 5.0x10^8 Pa and Young's      modulus is 4x10^11 Pa.                                                  (a) How much can the rod be stretched before exceeding its elastic      limit?                                                                                                                                         'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS1306      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒════════════════════════╕                                              │ SERIES and INTEGRATION └──────────────────────────────────────────────                                                                        8.00       Circumference of an Ellipse: Calculation by Series and                Integration                                                    ────────────────────────────────────────────────────────────────────────                                                                                 The circumference of an ellipse with axes lengths of "a" and            "b" as measured from its origin cannot be expressed in a simple         "closed" form by a formula.  The approximate value is                   calculated as:                                                                                                                                         l ≈ 2 * pi * sqr( (a^2 + b^2)/2 )                                                                                                        Thus if a = 50 and b = 10, the circumference, l ≈ 226.5.  The           circumference can be express "exactly" by use of the elliptic           integral of the second kind E(k,Φ):                                                                                                                    l = 4 * a * E(k,Φ)   k= sqr( abs(a^2-b^2) )/a                                                                                            There are at least two methods to obtain a higher degree of             accuracy:  the first is to use a series expansion for E(k,Φ)            and the second is to numerically integrate E(k,Φ).  The                 following two examples show how AstroFormCalc 3 can be used to          sum up a series or to accurately integrate an equation.  The            methods are very general and are applicable to many problems in         Physics as well as virtually all other disciplines.  It should          be noted that the "approximation" formula, given above, is only         accurate to about 8%.                                                                                                                  Topic # 21: SERIES, ARC LENGTH (CIRCUMFERENCE) OF ELLIPSE                                                                                       Discussion: Estimate the circumference of an ellipse with axes lengths   of 50 and 10 cm as measured from its origin. Use the series             approximation.                                                                                                                                 'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSELSE      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 22: INTEGRATION, ARC LENGTH (CIRCUMFERENCE) OF ELLIPSE                                                                                  Discussion: Estimate the circumference of an ellipse with axes lengths   of 50 and 10 cm as measured from its origin. Use the elliptic integral  method.                                                                                                                                        'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSELIN      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═════════════════╕                                                     │ IDEAL GAS LAW   └─────────────────────────────────────────────────────                                                                        9.00         Ideal Gas Law Calculations.                                ────────────────────────────────────────────────────────────────────────                                                                                 The behavior of gases at high temperatures and low pressures is         approximated very well by the ideal gas law which combines              Boyle's pressure-volume behavior and Charles' temperature               behavior of ideal gases into a single expression.  The                  following templates are written in a general form which allows          calculation of the "missing" variable from a properly defined           gas problem.                                                                                                                           Topic # 23: IDEAL GAS, PRESSURE, VOLUME, TEMPERATURE, MOLES, GRAMS,      MOLECULAR WEIGHT, DENSITY                                                                                                                      Discussion: Find the density in grams per liter of water at STP.                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSGAS1      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 24: IDEAL GAS, PRESSURE, VOLUME, TEMPERATURE, MOLES, GRAMS,      MOLECULAR WEIGHT, DENSITY                                                                                                                      Problem # 24.1: 3 grams of an unknown gas exert a pressure of 0.2654     atm at T=273 K in a 5.5 liter gas cell.                                 (a) What is the molecular weight of the gas?                                                                                                   'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSGAS2      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒══════════════╕                                                        │ ELECTRICITY  └────────────────────────────────────────────────────────                                                                        10.0       Resistance and Capacitance.                                  ────────────────────────────────────────────────────────────────────────                                                                        Topic # 25: RESISTANCES, SERIES and PARALLEL EQUIVALENTS                                                                                        Discussion:                                                                                                                                                                                                             series      ---/\/\/\---/\/\/\---/\/\/\--...   =     ---/\/\/\---       equivalent       R1       R2       R3                    RS                                                                                                                                                             parallel                                                                equivalent   __________________________....                                              |        |        |                      |                              >        >        >                      >                              < R1     < R2     < R3        =          < RP                           >        >        >                      >                              |        |        |                      |                          ---------------------------...                                                                                                                                                                              Note: for parallel equivalents, resistances=0 are not included.                                                                                'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSRESP      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 26: RESISTANCES, SERIES and PARALLEL EQUIVALENTS                                                                                        Discussion: Find the equivalent resistance of the circuit shown below.                                                                                     |---/\/\/\---|                                                          |    150     |                                                     |----|---/\/\/\---|---/\/\/\---|                                        |    |    150     |     50     |                                     o--|    |---/\/\/\---|            |--o                                     |         150                  |                                        |              100             |                                        |-------------/\/\/\-----------|                                                                                                                                                                                                                                                                                                                                  'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS2510      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 27: CAPACITANCES, SERIES and PARALLEL EQUIVALENTS                                                                                       Discussion:                                                                                                                                                     | |       | |      | |                   | |            series      ----| |-------| |------| |---...   =     ----| |-----       equivalent      | |       | |      | |                   | |  CS                        C1        C2       C3                                                                                                           parallel                                                                equivalent   __________________________....                                              |        |        |                      |                              |        |        |                      |                            ----- C1 ----- C2 ----- C3      =        ----- CP                       -----    -----    -----                  -----                            |        |        |                      |                              |        |        |                      |                          ---------------------------....                                                                                                                                                                             Note: for series equivalents, capacitances=0 are not included.                                                                                 'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSCASP      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═════════╕                                                             │ OPTICS  └─────────────────────────────────────────────────────────────                                                                        11.0       Geometric Optics: Lenses and Mirrors                         ────────────────────────────────────────────────────────────────────────                                                                        A "thin lens" is shown below. Surface is represented by 's'.                                                                                                         ss                                                                     s  s                                                                    s  s                     M[T] + means erect image     ╦ Y[O]           s    s                                                 ║······o·········s····s········o··········o  S source point             S     F[O]       s    s       F[I]   Y[I] ║  P image point                                s  s                    ╩  S[O] Source distance       |·X[O]·|···f····· s  s·····f···|····X[I]··|  S[I] Image distance                           ss                                                   |--------S[O]------|-----------S[I]-------|                                                                                                   Sign Convention:  X[O] + means its left of F[O]        focal_length < 0                   X[I] + means its right of F[I]           means                   Y[I], Y[O] + means above optical axis        diverging lens.                                                                                  The following problem uses the Gaussian or lensmaker formula to         calculate focal lengths and magnifications for various kinds of         lenses.  Convex lenses are converging and concave lenses are            diverging.                                                                                                                             Topic # 28: THIN LENS IMAGERY, CHARACTERISTICS for REAL OBJECTS,         GAUSSIAN                                                                                                                                       Problem # 28.1: A 10 cm tall statue of Curly Howard is sitting 100 cm    from a positive (converging) lens of 30 cm focal length.                (a) Describe Curly's image.                                                                                                                    'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS420       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                                                                                         A spherical mirror is shown below. Mirror surface is represented by 's'.                          s                                                                   · o·                   S = source object                         ·  °    s °                   V = vertex of sphere               ·  °          s   ° P     C          P = image (between F and C)S ·°· · · · · · · · ·o· · ·°o · · o          R = 2 * F                  |                   V|s     |  ·°                                       |                    | s   ·|°  R      S[O] = distance S to vertex      |                    |  s°  |         S[I] = distance vertex to image   |-------S[O]---------|-S[I]-|    C = center of sphere R = radius curvat.                                                                        Sign Convention: S[O] + means its left of vertex V, focus + means concv                  S[I] + means its left of vertex V, focus - means convex                 R    + means center C is right of V                                                                                                     A problem on mirror design follows.                                                                                                    Topic # 29: SPHERICAL REFRACTING MIRRORS, IMAGE vs MAGNIFICATION                                                                                Problem # 29.1: An eraser 5 cm tall sits 150 cm in front of a concave    mirror of focal length 400 cm.                                          (a) Describe the image.                                                                                                                        'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYS495       ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒══════════════╕                                                        │ AC CIRCUITS  └────────────────────────────────────────────────────────                                                                        12.0       Impedance and Radio Frequency Matching                       ────────────────────────────────────────────────────────────────────────                                                                        Topic # 30: INPUT IMPEDANCE, LOSSLESS COAXIAL CABLE, LOAD IMPEDANCE                                                                             Discussion: Input resistance RIN (in Ohms) and reactance XIN (in Ohms)   looking into coaxial cable of length LENGTH (in cm) and D1 (in          wavelengths), velocity factor VF, characteristic resistance Z0 (in      Ohms), and terminated in a load inductance LLOAD (in uHenries) or       capacitance CLOAD (in pFarads) in series with a resistance RLOAD (in    ohms) at frequency F0 (in megaHertz).                                                                                                                                                ________________                               |--- length ---------|   |           ---|---                             ____________________    |           │xload│                      o-----(____________________(---|           ---|---                  Rin        coax, char. imp. Z0                    \                                                                       / rload               Xin o---------------------------------------------|                                                                                                                                                                                                                                          'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSRFMA      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 31: SERIES RESONANT CIRCUIT, RF MATCHING, INDUCTIVE LOAD,        RESISTIVE INPUT                                                                                                                                Discussion: Calculates values of capacitances C1 (in pFarads) and C2     (in pFarads) required to tune or match an inductive load consisting of  an inductance LLOAD (in uHenries) and a pure resistance RLOAD (in       Ohms) to a pure input resistance RIN (in Ohms) without reactance at     frequency F0 (in megaHertz).                                                                                                                                                       | |                                               o------------|--------| |-------------|                                              |        | | C1          ) lload                      Rin            -------         (pF)        ) (uH)                     Xin=0            -------                     |                                              |  C2                    \                                              | (pF)                   /  rload                          o------------|------------------------|  (Ohms)                                                                                                                                                                                                                                                                                                           'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSTSTC      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════════╕                                                       │ USEFUL CALCs  └───────────────────────────────────────────────────────                                                                        13.0 Useful Calculations for Problem Solving in Applied Physics.        ────────────────────────────────────────────────────────────────────────                                                                                 ARITHMETIC and GEOMETRIC PROGRESSIONS                                                                                                           A progression is a sequence of numbers, called TERMS, in which          any term can be obtained from its predecessor by adding,                subtracting, multiplying by or dividing by a fixed number.              When terms are generated by adding/subtraction a fixed number           called the COMMON DIFFERENCE, the progression is called                 ARITHMETIC.  When terms are generated by multiplying/dividing           by a fixed number called the RATIO, the progression is called           GEOMETRIC.  Many financial calculations are based on the                concept of the progression.                                                                                                                     The following example illustrate an arithmetic progression with         a common difference of 4 between terms.                                                                                                ----------------------------------------------------------------------- Arithmetic progression: 4, 8, 12, 16, ...   (common difference = +4)                                                                            com. diff.       +4 =   +4 =   +4 =   +4 =    +4 =    +4 =    +4 =                                                                              term           4      8     12     16     20      24      28      32 ...                                                                        index          1st    2nd   3rd    4th    5th     6th     7th     8th   -----------------------------------------------------------------------                                                                                  To generate a progression, one need only specify any two terms,         their values and positions (or indices).  (Note, they don't             even have to be adjacent!).                                                                                                            Topic # 32: ARITHMETIC PROGRESSION                                                                                                              Discussion: A sequence of numbers in which any number, or term, after    the first can be obtained by adding a fixed number COMMDIFF to its      predecessor. Example 12, 22, 32, 42... or 27, 25, 23, 21... To solve    for progression enter any two term positions INDEX#A and INDEX#B and    their values TERM#A and TERM#B. TERM#N is the value for any index N     and SUM is the sum of the progression up to and including term N.                                                                              'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSARPR      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                          The following examples illustrate a geometric progression with          a common ratio of 2, respectively, between terms.  Note:  '*"           means to multiply and '/' means to divide.                                                                                             ----------------------------------------------------------------------- Geometric progression: 4, 8, 16, 32, ...   (common ratio = +2)                                                                                  com. ratio       *2 =   *2 =   *2 =   *2 =    *2 =    *2 =    *2 =                                                                              term           4      8     16     32     64     128     256     512 ...                                                                        index          1st    2nd   3rd    4th    5th     6th     7th     8th   -----------------------------------------------------------------------                                                                                  To generate a progression, one need only specify any two terms,         their values and positions (or indices).  (Note, they don't             even have to be adjacent!).                                                                                                            Topic # 33: GEOMETRIC PROGRESSION                                                                                                               Discussion: A sequence of numbers in which any number, or term, after    the first can be obtained by multiplying its predecessor by a fixed     number COMMRATIO. Example 12, -24, 48, -96... or 27, 9, 3, 1... To      solve for progression enter any two term positions INDEX#A and INDEX#B  and their values TERM#A and TERM#B. TERM#N is the value for any index   N and SUM is the sum of the progression up to and including term N.                                                                            'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSGMPR      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 Topic # 34: EXACT TIME, APPROXIMATE TIME                                                                                                        Discussion: Exact time is the exact number of days while approximate     time assumes 30 days per month. ADAY1, AAMONTH1 and AYEAR1 is first     date and BDAY2, BBMONTH2 and BYEAR2 is the second or last date. Enter   month as a number: Jan=1, Feb=2, March=3, April=4, May=5, June=6,       July=7, Aug=8, Sept=9, Oct=10, Nov=11 and Dec=12. EDAYS is exact days   between two dates (but not including last day, add 1 to including last  day). ADAYS is approximate days. For example, April 20, 1993 is         entered as AAMONTH=4, ADAY1=20, AYEAR1=1993.                                                                                                   'EQU               ≡ ** If highlighted, type Q to get equations that ** 'EGE PHYSEDAY      ≡ ** solve this problem. Scroll down to highlight.**                                                                                                                                                 ╒═══════════╕                                                           │ GLOSSARY  └───────────────────────────────────────────────────────────                                                                        14.0     Glossary of Terms                                              ────────────────────────────────────────────────────────────────────────                                                                               ║ Note, Use the Jump command to locate a glossary reference.    ║       ║ Scroll the screen until the reference is in the middle at line║       ║ 12.  The Jump box will light up.  Type J to locate.  Repeat   ║       ║ typing A, as needed, to continue the search.                  ║                                                                        Acceleration in a straight line.  See PHYS3P2.                                                                                                Arithmetic progression.  See PHYSARPR.                                                                                                        Capacitance, parallel.  See PHYSCASP.                                                                                                         Capacitance, series.  See PHYSCASP.                                                                                                           Distance in a straight line.  See PHYS3P11.                                                                                                   Elasticity.  See PHYSYMOD.                                                                                                                    Elastic limit. See PHYS1306.                                                                                                                  Geometric progression.  See PHYSGMPR.                                                                                                         Gravity.  See PHYSUNMO.                                                                                                                       Ideal Gas Law.  See PHYSGAS1.                                                                                                                 Integration.  See PHYSELIN.                                                                                                                   Lenses.  See PHYS420.                                                                                                                         Matching, RF.  See PHYSRFMA.                                                                                                                  Mirrors.  See PHYS495.                                                                                                                        Network, capacitance.  See PHYSCASP.                                                                                                          Network, resistance.  See PHYSRESP.                                                                                                           Pythagorean Theorem.  See PHYS2P16.                                                                                                           Resistance, parallel.  See PHYSRESP.                                                                                                          Resistance, series.  See PHYSRESP.                                                                                                            Series.  See PHYSELSE.                                                                                                                        Strain.  See PHYSYMOD.                                                                                                                        Stress.  See PHYSYMOD.                                                                                                                        Tuning, RF.  See PHYSRFMA.                                                                                                                    Vector addition.  See PHYSVECT.                                                                                                               Velocity in a straight line.  See PHYS3P2.                                                                                                    Young's modulus.  See PHYSYMOD.                                                                                                               ╒═════════╕                                                             │ LICENSE └─────────────────────────────────────────────────────────────                                                                        15.0             Product License and Warranty.                          ────────────────────────────────────────────────────────────────────────                                                                                            Software License Agreement                                                                                                           PCSCC grants you the right to use this Software for a                   single-user computer or a workstation not attached to a                 network.  You may not rent or lease this Software without the           expressed written permission of PCSCC.  You may not decompile,          disassemble, reverse engineer, copy, create a derivative work,          or otherwise use this Software except as stated in this                 agreement.  The license authorizes you to create and use an             extra copy of the Software on a home or laptop computer, as             long as the extra copy is never loaded at the same time this            Software is loaded on the primary computer on which you use             this Software.                                                                                                                                  If any provision of this agreement is found to be unlawful,             void, or unenforceable, then that provision shall be severed            from this Agreement and will not affect the validity and                enforceability of any of the remaining provisions.  This                agreement shall be governed by the laws of the State of                 Delaware.                                                                                                                                       The Software and accompanying materials are provided with               Restricted Rights.  Use, duplication, or disclosure by the              Government is subject to restrictions as set forth in                   subparagraph (c) (1) (ii) of The Rights in Technical Data and           Computer Software clause at DFARS 252.227-7013, or                      subparagraphs (c) (1) and (2) of the Commercial Computer                Software--Restricted Rights at 48 CFR 52.227-19, as applicable.         Contractor/manufacturer is PC SuperComputer Capital,                    Incorporated, at the address listed below.                                                                                                      Type T to return to the Table of Contents.                                                                                                                       Warranty Information                                                                                                           PC SuperComputer Capital, Inc.  (PCSCC) hereby disclaims all            warranties relating to this Software, whether express or                implied, including without limitation any implied warranties of         merchantability or fitness for a particular purpose.  PCSCC             will not be liable for any special, incidental, consequential,          indirect or similar damages due to loss of data, loss of                profits, lost savings or any other reason, even if PCSCC or an          agent of PCSCC has been advised of the possibility of such              damages.  In no event shall PCSCC's liability for any damages           ever exceed the price paid for the license to use Software,             regardless of the form of the claim.  The person using the              Software bears all risk as to the quality and performance of            the Software.  This Software is licensed AS IS.                                                                                                 Any action or proceeding brought by either party against the            other arising out of or related to this agreement shall be              brought in a STATE or FEDERAL COURT of competent jurisdiction           located in Fairfield County, Connecticut.  The parties hereby           consent to in personam jurisdiction of said courts.                                                                                             Type T to return to the Table of Contents.                                                                                             ╒═══════════════╕                                                       │ PRODUCT  INFO └───────────────────────────────────────────────────────                                                                        16.0     Product Information and How to Order Complete Package.         ────────────────────────────────────────────────────────────────────────                                                                                 AstroFormulaCalculator 3 Product Description 8-1-1993                                                                                           AstroFormulaCalculator 3 is a unique and innovative mathematics         tool which offers productivity enhancements not found in any            other software package either retail or shareware.  This                hands-on program combines the functions of both a spreadsheet           and calculator; but it is better.  Why?  Because it is right            between the two:  Easier than a spreadsheet and more powerful           than a calculator.  With its special format-free interface,             formula or equation-based iterations are much easier to set up          than in a spreadsheet.  It is designed to be "smarter" which            makes it very user-friendly for Professionals of all levels,            especially for the infrequent or "computer-shy" user.  Broad            applications exist in many disciplines where calculations with          formulas, equations or other math recipes are required such as          in Economics, Genetics, Chemistry, Electrical Engineering,              Engineering Mechanics, Fluid Mechanics & Hydraulics, Finance,           Physics, Statistics and even Nursing.  Features include:                                                                                        ∙ DOS or Windows as non-Windows application.  Runs on all PC            compatibles.  DOS 2.1+, Monochrome display, 200K RAM, floppy or         disk.                                                                                                                                           ∙ DOS command line support for any direct calculation such as           addition, multiplication, subtraction and division.                                                                                             ∙ Format-free entry of up to 63 equations with at least 256             independent variables and 256 constants.  Smart and                     "hassle-free" interpreter.                                                                                                                      ∙ Equations and formulas are written according to the BASIC             conventions.  Versatile library of built-in functions.                                                                                          ∙ Advanced calculator functions including many automated                numerical methods such as:                                                                                                                      ∙ Newton-Raphson for solving x in y=f(x)                                ∙ Advanced simplex for solving x at W=Y=Z in W=f(x), Y=g(x),              Z=h(x)                                                                ∙ Numerical integration (two methods)                                   ∙ Numerical differentiation                                             ∙ Summation                                                             ∙ Finding maxima and minima                                             ∙ Plotting equations                                                    ∙ Saving/retrieving data files with full file management                  support                                                               ∙ Screen dumps as DOS text files for inclusion in documents                                                                                     ∙ Highly-structured documentation, on-line with Table of                Contents, Glossary and search function.  Interactive with               program.                                                                                                                                        ∙ On-line helpfile.  Comprehensive summary of                             commands/functions with step-by-step examples on uses of all            advanced functions.                                                   ∙ On-line user manual.  A "learn by example" document which               illustrates the universal nature of problem-solving with many           step-by-step examples from Science, Engineering and Finance.                                                                                  ∙ Full support for ACTION21 and ACTION11 data sets.                                                                                             ∙ Comments from users:                                                                                                                   ∙ "... calculate circuit board drilling and routing speeds...easy to       use, versatile and powerful with good documentation."                                                                    J. L.  New York     ∙ "...used the integration capability to determine defect density...do     not have any tool (either PC or host based) that does for me what       ...(AstroFormCalc 3)...does."                                                                                            J. R.  Virginia     ∙ "...for Electrical Engineering practice it is better than a              spreadsheet and a calculator..."                                                                                         C. B.  Florida      ∙ "...used to do frequency spectrum work and calculations on circuits,     ...of real value and a productivity tool."                                                                               E. S.  California   ∙ "...one of a handful of scarcely available packages...in the types       of numeric problems they solve."                                                                                         W. C.  Chile                                                                                       This productivity-enhancing tool has been developed by the team         at PC SuperComputer Capital, Inc.  Order the complete version           of AstroFormulaCalculator 3 today!                                                                                                     ╒════════════════╕                                                      │ OTHER PRODUCTS └──────────────────────────────────────────────────────                                                                        17.0                 Other Astro 3 Products                             ────────────────────────────────────────────────────────────────────────                                                                                 All Astro 3 application files and data sets are fully                   compatible among all members of the Astro 3 family of                   professional software which include:                                                                                                      ∙ AstroEquationSolver 3 - Solves both linear and nonlinear                    simultaneous equations with up to 30 unknowns.  Characterized           by extremely easy setup.  Uses active/inactive method of                AstroFormulaCalculator 3 to select variables.  Includes program         ASOL3.EXE, on-line help file ASOL3HLP.HLP and on-line User              Manual ASOL3MAN.HLP.  (Available in December, 1993.)                                                                                      ∙  AstroDataFitter 3 - Fit data to any algebraic expression.                  Nonlinear optimization.  Up to 30 "active" variables.  Up to            500 data points.  "Smart" algorithm requires minimal user input         to solve problems.  DOS text plots of "fit".  Point-by-point            listing of fitted data.  Residual variance, correlation                 coefficient and much more.  Includes program AFIT3.EXE, on-line         help file AFIT3HLP.HLP and on-line User Manual AFIT3MAN.HLP.            (Available in December, 1993.)                                                                                                            ∙  AstroShadowBox 3 -  The pop-up resident member (TSR) of the Astro          3 team.  Provides math support for other DOS programs.  Pop-up          via hot key, surround calculation in "shadow box", and type             "(enter)" to pass result down through keyboard buffer.                  Extensive feature also include screen dumps with append as DOS          text files or as parsed 123 (tm, Lotus) .WK1 files.  Includes           program ABOX3.EXE, on-line help file ABOX3HLP.HLP and on-line           User Manual ABOX3MAN.HLP.  (Available in December, 1993.)                                                                                 ∙  AstroUtility 3  -   Support for authors to construct their own             on-line application help files.  Develop a simplified                   .LST file which supports all apostrophe commands and allows             construction of interactive applications which contain                  "load-and-go" equations or reference .EQU files.  Automatic             Table of Contents and line numbering.  Up to 64,000 lines.              (Available in December, 1993.)                                                                                                                  See below for instructions on ·Registration·.                                                                                          ╒══════════════╕                                                        │ REGISTRATION └───────────────────────────────────────────────────────                                                                         18.0                 Order/Registration Form                            ────────────────────────────────────────────────────────────────────────                                                                                 If a printer is available, position the order form (part 1) on          the screen and type the "(print screen)" key to make a copy.            Then, advance the text and position the order form (part 2) on          the screen and type "(print screen)" again to finish.                                                                                                  ASTRO3 Products Order/Registration Form  (part 1)                                                                                   Name:________________________________  Title:________________                                                                                   Company:_____________________________________________________                                                                                   Address:____________________________ City:___________________                                                                                   State:___________   Zip:_____________  Country:______________                                                                                   Date:_____/_____/_____           (Fill out form completely)                                                                                     ---------------------------------------------------------------         Product                     #     Price/ea     S&H       Total          ---------------------------------------------------------------         AstroFormulaCalculator 3   ___    _$29.95_    _$5.00_   _______         AstroEquationSolver 3      ___    _$59.95     _$5.00_   _______         AstroDataFitter 3          ___    _$59.95_    _$5.00_   _______         AstroShadowBox 3           ___    _$59.95_    _$5.00_   _______         AstroUtility 3             ___    _$59.95_    _$5.00_   _______                                                              ----------     ------------------------------------------------------------------------------------------------------------------------------------------------                ASTRO3 Products Order/Registration Form  (part 2)                                                                                   * Canadian Orders, Add $2.00 per copy                   _______                                                                                 * International Orders, Add $6.00 per copy              _______                                                                                 * CT Residents add appropriate sales tax                _______                                                                                                                  TOTAL ENCLOSED      __________                                                                                 Disk Size: [ ] 5-1/4"   [ ] 3-1/2"   [ ] Check  [ ] Visa  [ ] MC                                                                                Card# __________________________________     Exp. Date ________                                                                                 Signature ______________________________                                                                                                        How did you hear about our Products?    [ ] BBS   [ ] Friend            [ ] Other _____________________________________________________                                                                                               Mail Completed form with Payment to:                                                                                                                  PCSCC, Inc.   Dept. PHCA                                                   P. O. Box 173                                                        Botsford,  CT   06404  USA                                                                                                  Support ONLY,  1-203-270-9079     E-mail to CIS, 72263,1657                                                                                        [October 1993]  Prices subject to change without notice.                                                                                                Type T to return to the Table of Contents.                                                                                       ╒═════════════════════╕                                                 │ MANUAL INSTALLATION └─────────────────────────────────────────────────                                                                        19.0           Instructions for Manually Installing Package.            ────────────────────────────────────────────────────────────────────────                                                                             The following are minimal instructions for manually installing                                 AstroFormulaCalculator 3.                                                                                           ∙ Minimum distribution files:  README.1ST, ACAL3.ICO, ACAL3.EXE,          ACAL3HLP.HLP, PHYCAL.HLP and *.EQU.                                                                                                           ∙ These files will probably be bundled in a compressed file such as       PHYCAL.ZIP, PHYCAL.SDN, or something similar.  Please unload.                                                                                 ∙ Create a DOS directory named ASTRO3 and change to it:                   cd\ (enter)    md\astro3 (enter)  cd \astro3 (enter)                                                                                          ∙ Copy ACAL3.EXE, ACAL3HLP.HLP, ACAL3.ICO and PHYCAL.HLP and *EQU         into the directory ASTRO3                                                                                                                     ∙ Add these statements to AUTOEXEC.BAT in the base directory:             SET ASTRO3=C:\ASTRO3                                                    append to existing PATH statement  ;C:\ASTRO3;                                                                                                ∙ Running Under Windows as a Non-Windows Application                                                                                             Follow the installation instructions and install on the hard drive C.   Start WINDOWS (tm, MicroSoft).  Click on FILE then click on PROPERTIES. Enter the following information for each of the fields.  Description:   AstroFormCalc 3, Command:  ACAL3.EXE, Working Directory:  \ASTRO3.      Click on CHANGE ICON.  Enter Filename:  C:\astro3\acal3.ico.  Click on  OK to exit and click on OK to exit FILE.  The AstroFormCalc 3 icon      should appear in the accessory window.  Click on it to run ACAL3.                                                                              ∙ To start from DOS:  cd\astro3 (enter)  then  PHYCAL (enter)             or:                 acal3 \astro3\PHYCAL.hlp (enter)                                                                                          ∙ To start with the on-line help file, type                                                   cd\astro3 (enter) then acal3 ? (enter)                                                                                    ╒═════════════╕                                                         │ AUTHOR ???? └─────────────────────────────────────────────────────────                                                                        20.0           Interested in Becoming the Author of Your Own                         Interactive Application File?                              ────────────────────────────────────────────────────────────────────────                                                                                 Many technologies are based on math/algebra.                            AstroFormulaCalculator 3 and its interactive, problem-solving           application files offer distinct advantages to the Author.  The         *.EQU templates are easy to develop and PCSCC offers complete           support for compiling these into the interactive application            files such as the help file PHYCAL.HLP which you are                    currently reading and the help file ACAL3HLP.HLP which                  accompanies this program.  Application files can be written for         any level of user from the very beginner to the Ph.D.  Contact          PCSCC for more information.  To automatically jump to our               address, type "J" if the jump bar is highlighted on the                 following words mail completed form.                                                                                                 ╒═══════════╕                                                           │ HELP FILE └───────────────────────────────────────────────────────────                                                                        21.0           Help File: Summary of File Viewing Commands              ────────────────────────────────────────────────────────────────────────                                                                            A - Auto-search of entire text for user-supplied string. Search is          in uppercase and is case insensitive. If string found,                  type A to continue or to enter new string, type (space) A.          B,N - Move back or ahead 18 lines.  Also use (backspace) for "B".       E, (esc) - Exit from help file to equations display.                    F,T,K - Jump to the first (beginning), T.O.C or last (end) line.        G - Skip to Glossary of terms or summary of functions, if present.      J,(ent) - Search line on │JUMP│, Reference is after . Jump to                    line number or perform autosearch ahead if text reference.    L,P - Jump to line/page. Type Lxxx(ent) or Pyy(ent) to jump to                line #xxx or page #yy. With + or -, ahead or back 56 lines.       S,R - Skip ahead (S) or back (R) in help file to major headings         W - Skip to Summary of useful calculations or warnings, if present      1 to 9 - Typing 1 to 9 advances the text by 1 to 9 lines.               (ctrl Q) - Exit from help file.  Same as command "E".                   Edit keys - Use edit keys: (Home) (up arrow) (PgUp) (left arrow)                    (right arrow) (End) (down arrow) (PgDn).                                                                                             Entry into the application file is at/near the last position.           Type: T to return to Table of Contents or E to exit the file.      