Manual / Guide · 1982
TRS-80 Pocket Computer Engineering Math II
The manual for Radio Shack's Engineering Math II software for the Pocket Computer.
Manual / Guide · 1982
The manual for Radio Shack's Engineering Math II software for the Pocket Computer.
TRS-8O0 POCKET COMPUTER | SOFTWARE 9eSe-92 ‘ON iva = <q o o re] o a = re, 2 ro = o IL iL! = oc 4 iL! ~ INSTRUCTION MANUAL Engineering Math Il Radio Shaek A DIVISION OF TANDY CORPORATION FORT WORTH, TEXAS 76102 Engineering Math II Program: ©1981 Tandy Corporation All Rights Reserved. Engineering Math Il Program Manual: ©1982 Tandy Corporation All Rights Reserved. Reproduction or use, without express written permis- sion from Tandy Corporation, of any portion of this manual is prohibited. While reasonable efforts have been taken in the preparation of this manual to assure its accuracy, Tandy Corporation assumes no liability resulting from any errors or omissions in this manual, or from the use of the information obtained herein. Please refer to the Software License on the inside back cover of this manual for limitations on use and reproduction of this Software package. 10987654321 Table of Contents Introduction .................0000.000, 4 Vector Arithmetic .........0..0.0...00.. 2 Clear eee ee eee ee 2 Add oo. eee cece cece ee 3 Subtract... 0... eee 3 Dot Product ..............0.00.00. 3 Cross froduct ene e reece eee nes 3 Angie Computation................ 3 Polar to. Rectangular Coordinate Conversion ........ 3 Rectangular to Polar Coordinate Conversion ........ 3 Change Mode .................... 3 Variable List... 0.00. 0...0...00...00. 4 Complex Arithmetic for the Pocket Computer ............. 5 Variable List... ......0.0........000. 7 Advanced Trig and Exponentiation ............... ModeS... 0.0... eee aes Changing the Mode............ Using the Trig Functions ........... Using the Logarithm Function....... Exponentiation Permissible Numerical Ranges for Functions ................. Variable List... 0... eee eee Appendices A—Functions of the Engineering Math Packages B—Making a Backup C—Maintenance.................. Introduction Engineering Math II consists of three programs: Program Description VECTOR Vector arithmetic COMPLEX Complex arithmetic ADVMATH Advanced trig and exponentials The functions of the programs are as follows: t VECTOR provides all common vector operations in three dimensions in both Cartesian and polar coordinates: addition, subtraction, dot product, cross product, angle between two vectors, and direct conversion of a vector between rectangular and polar coordinate systems. Chain operations are allowed. The mode may be changed between polar and rectangular at any point during program execution without adversely affecting intermediate results. COMPLEX provides for the most common complex number arithmetic operations: addition, subtraction, multiplication, division, calculation of magnitude, conjugation, base-e logarithms, e to complex powers, sines, cosines, arc sines, and arc cosines. Chain operations are allowed. ° ADVMATH provides 24 common trig functions in degree or radian measure. It also provides logarithms to any base and an exponentiation function which can raise negative numbers to positive or integral negative powers. At the end of each section of the manual, there is a description of the program variables. These may be useful if you want to examine intermediate results. Use the Backup instructions in Appendix B to make a working copy of the tape. See Appendix C for Maintenance instructions. Vector Arithmetic This program will perform most common vector operations in three dimensions. it can use either rectangular or polar coordinates, and in the polar mode can use radian, degree, or grad units of arc. To joad VECTOR, insert the tape in the recorder and press the ‘Play’ key. Turn the computer on, make sure the mode is set to DEF, then type: ODOM BCAMEAMAO A and press CEN . After the prompt sign (>) appears, press GHFTSPC). The program will start itself in the rectangular mode. First, it will display the program title: VECTOR ARITHMETIC. Press CENTER) and the copyright notice will be shown briefly before the menu starts. _. Press ENTER) to see the available operations one at a time, along with the shift-letter command which will start each operation. These are: CLEAR: SHFT-C ADD: SHFT-A SUBTRACT: SHFT-S DOT PRODUCT: SHFT-D CROSS PRODUCT: SHFT-X ANGLE COMPUTATION: SHFT-V POLAR TO RECT: SHFT-F RECT 70 POLAR: SHFT-G CHANGE MODE: SHFT-M SHFT-K TO RE-ENTER MENU if the end of the menu is reached, the program will end. This is to prevent repeated listings of the menu if the Pocket Computer has a printer attached. (SHE TC) will restart the menu without restarting the program. The same input routine is used for all operations. The first display will be: FIRST VECTOR. it will then ask for X, Y, and Z (rectangular mode) or MAGNITUDE, PHI, and THETA (polar mode). SECOND VECTOR wiil be displayed and the input routine will be repeated. Starting any option will cause the program to ask for any needed information, display the results, then stop and await the next command. For chained Operations, such as a series of additions, press CENTER) in response to the first input question (X? or MAGNITUDE?, depending on the mode). This will cause the result of the last calculation to be loaded as the first operand. Clear will also reset the mode to rectangular. Add Press (SHF T)(A) to add one vector to another. Subtract Press (SHF T)CS) to subtract one vector from another. Dot Product Press (SHF 1)(D) to calculate the dot product of two vectors. Cross Product Press (SHET (XD) to calculate the cross product of two vectors. Angle Computation Press (SHE 1) to calculate the angle between two vectors. Polar to Rectangular Coordinate Conversion Press (SHFT) to convert a vector from polar to rectangular coordinates. This operation is independent of the set mode and does not affect any of the temporary resuits held by the computer. Note: This routine will call the input routine fora single vector. You must enter the vector you want to convert in response to the FIRST VECTOR statement. Rectangular to Polar Coordinate Conversion Press SHF T)(G) to convert a vector from rectangular to polar coordinates. This operation is independent of the set mode and does not affect any of the temporary results held by the computer. Change Mode Press (SHE TM) to switch modes from rectangular to polar or from polar to rectangular. The new mode will be displayed briefly. This operation does not affect the contents of the accumulator. In rectangular mode, all input and output is in terms of magnitude, phi, and theta, where phi is the clockwise angle from the X axis to the projection of the vector on the XY plane, and theta is the angle from the XY plane to the vector. Exampis (1x + 2y +3z) + (-2x+1y—z) = (—1x+ 3y + 22) Computer displays: You type: > (SHETA) FIRST VECTOR Displays briefly X? COENTER) Y? ENTER) 2? (@XENTER) SECOND VECTOR Displays briefly XP OOG@XENTER) Y? COCENTER) 2? COCIENTER) X=-1.° CENTER) Y=3. (ENTER) Z=2, CENTER) > Variable List A—X In Accum B—Y In Accum C—Z In Accum X—X Y-Y Z—Z G-I—Dummies and Holders J—Magnitude K—THETA L—PHI M—Mode: 0 = RECTANGULAR, 1 = POLAR N-P—Holders Q—Early Return Flag R—Holder Complex Arithmetic for the Pocket Computer This program allows complex numbers to be added, subtracted, multiplied, divided, or conjugated. It also allows for the calculation of natural (base-e) logarithms, natural anti-logarithms, sines, cosines, arc sines, and arc cosines. These functions may be used in conjunction with the program’s chaining capability to complete almost any calculation. Please note that this program starts and runs only in RADIAN mode. All trig and exponential functions assume radian input and display radian resuits. Attempting to reset the mode to DEGREE or GRAD will result in inaccuracies in trig and exponential functions. i To load COMPLEX, insert the tape in the recorder and press the “Play” key. Turn the computer on, make sure the mode is set to DEF, then type: ODOAMMAIOM RDC and press (ENTER). After the prompt sign (>) appears, press (SHF T)\(SPC). The program title will be displayed: COMPLEX ARITHMETIC. Press ENTER) and the copyright notice will be displayed for about a second, then the command prompt will appear: > READY. The desired operation is selected by pressing the (GHET) key followed by a letter: to ADD, press (SHFT)(A) to SUBTRACT, press SHF TICS) to MULTIPLY, press GHF TM) to DIVIDE, press GHF T)(D) to CONJUGATE, press (SHF TC) to calculate MAGNITUDE, press (SHF T)(Z) to calculate Natural LOGARITHM, press G@HFT)L) to calculate Natural ANTILOG, press (G@HF TK) to calculate SINE, press (SHF T)CF) to calculate COSINE, press (GHF T)CG> to calculate ARC SINE, press G@HF TCH) to calculate ARC COSINE, press (SHF1T>GJ) to return to >READY, press (SHF TIX) to REDISPLAY LAST ANSWER, press (SHF TMG) The same input routine is used for all operations. In rectangular mode, the first question is: IST NUMBER REAL? Enter the real portion of the first number. Next is: 1ST NUMBER IMAGINARY? Reply with the imaginary part of the first number. If the chosen operation is monadic (one that requires only one operand), the input routine will end at this point. In polar mode, you are asked for magnitude and phase angle rather than real and imaginary components. Note: You may use the result of the last computation as an operand by pressing (ENTER) in response to: 1ST NUMBER REAL? {f this is done, the input routine will load the result of the last computation as the first operand of the new operation and skip to: 2ND NUMBER REAL? Next comes: 2ND NUMBER REAL? and 2ND NUMBER IMAGINARY? When all data has been entered, the computer will beep once when the answer is ready and display the result with the reat portion on the left half of the display and the imaginary portion on the right. The real and/or imaginary part of the second number may be kept unchanged by pressing (ENTER) in response to either: 2ND NUMBER REAL? or: 2ND NUMBER IMAGINARY? In either case, when CENTER) is pressed, the old value of the number asked for will be displayed briefly and retained. Computation of magnitude does not change the numbers stored by the program. Instead, magnitude is calculated and displayed separately. The magnitude is not kept as a new “1st number"; instead the complex number whose magnitude was computed is kept. You can combine the functions available in this program to evaluate many other factors. For example, 6 in raising a complex number to a complex power, recall that if we take the log of the first number, multiply that by the second, and raise e to the resulting power, we've effectively raised the first number to the second power. To raise 2+ 3i to the 5+2i power, we could conduct the following operations: Computer displays: You type: > READY HEFT) LOGARITHM Displays briefly 1ST NUMBER REAL? QiXENTER) 1ST NUMBER IMAGINARY? GICENTER) (BEEP) 1.282474679 9.82793E-01 GHEDM™) MULTIPLY Displays briefly 1ST NUMBER REAL? (ENTER) 2ND NUMBER REAL? (ENTER) 2ND NUMBER IMAGINARY? (2..ENTER) (BEEP) 4446785949 7.478917974 (SHFTVK) E“x Displays briefly 1ST NUMBER REAL? (BEEP) 31.26721338 79.41886041 Your Answer: 31.267 + 79.4191 ‘With this method and the COMPLEX program’s ability to chain easily (as demonstrated above), it can complete just about any calculation. Note: Not all complex math problems have unique answers. Operations such as logarithm have multiple but equally correct solutions; hence when this program conducts extraction of logs or an inverse trig function (which uses logarithms) the answer may not be the obvious one. Usually it will be—but the answer will always be a correct one. Just remember that it may not be the correct answer! The following algorithms are used: Conjugation: (A + Bi) = (A-Bi) Magnitude: = SQR(AA + BB) Addition: (A+ Bi) + (C+Di) = (A+C) + (B+ D)i Subtraction: (A+ Bi) - (C+ Di) = (A—C) + (B-D)i Multiplication: (A + Bi) * (C+ Di) = (AC— BD) + (AD + BC)i Division: (A + Bi) /(C + Di) = (AG + BD)(CC + DD) + (BC ~ AD)(CC + DD))i Logarithm: (compiex— examine code if interested) e to the z:e *(A+Bi) = e* A COS(B) + e “A SIN(B)i Sine: SIN(A + Bi) = (SIN(A)*(e * —B +e“ B)V/2 + (COS(A)*(e"B —e* — B)2i Cosine: COS(A + Bi) = (COS(A)(e* —B +e *B)/2 + (SIN(A)+(e * —B —e * B)V/2 i Arc sine: ASIN(Z) = —i Ln(i(Z+ SQR(ZZ— 1) Arc cosine: ACOS(Z) = —i Ln(Z+SQR(ZZ-— 1) When the result of the last computation is used as an operand, it is used as the first (A+ Bi in the algorithms). Variable List A—1st Number Real and Result Real B—1st Number imaginary and Result Imaginary C—2nd Number Real D—2nd Number Imaginary E—Holder for Incomplete Calculations and Magnitude F—Holder for Incomplete Calculations and Return Flag G—Holder for Incomplete Calcutations: Real H—Holder for Incomplete Calculations: Imaginary |—Error-Present Flag J—Single-Operand Flag K—Sign Flag in Inverse Sine/Cosine Computations Advanced Trig and Exponentiation This program allows the Pocket Computer to evaluate advanced trigonometric and exponential functions. To load ADVMATH, insert the tape in the recorder and press the “Play” key. Turn the computer on, make sure the mode is set to DEF, then type: ODOMODOMDOMMAAMDAHD| and press (ENTER). After the prompt sign (>) appears, press (SHF T)(SPC). The program name will be displayed first: ADVANCED MATH. Press to clear this display and start the menu, from which functions are called by number: (C) 1981 TANDY CORP. SELECT FUNCTION BY NUMBER: CHANGE MODE (RAD/DEG)O Note: This program does not send the menu to the printer. The following functions are provided: Number =‘ Function Abbreviation Ma Change Modes, DEG/RAD None @a Sine SIN Cosine cos 8 @@) Ba WMO) Me jene3) Mes Om @@ Me Ges) GG) @@ 1e-3e:3) @Qe GG) Qe “Tangent Cotangent Secant Cosecant Arc Sine Arc Cosine Arc Tangent Arc Cotangent Arc Secant Arc Cosecant Hyperbolic Sine Hyperbolic Cosine Hyperbolic Tangent Hyperbolic Cotangent Hyperbolic Secant Hyperbolic Cosecant Arg Hyperbolic Sine Arg Hyperbolic Cosine Arg Hyperbolic Tangent Arg Hyperbolic Cotangent Arg Hyperbolic Secant Arg Hyperbolic Cosecant LOGn(x) X to the Y TAN COT SEC csc ASIN ACOS ATAN ACOT ASEC ACSC SINH COSH TANH COTH SECH CSCH ASINH ACOSH ATANH ACOTH ASECH ACSCH LOGN none Any function may be called from any line of the menu. Modes The 12 circular trig functions may be evaluated in either degrees or radians, as set through program option 0. The 12 hyperbolic functions are always evaluated in radian measure, regardless of the mode. The current mode (DEG or RAD) is displayed near the top left of the Pocket Computer display window. Changing the Mode Enter option @). The mode will be changed. If it is RADian, it will change to DEGree. If the mode is DEGree, it will change to RADian. The new mode wilt appear in the top left of the display window. Using the Trig Functions Just call the function by number. The program will ask for the number to be evaluated: ARGUMENT?, then beep after calculations are compieted (this may take a couple of seconds) and display the answer. Pressing (ENTER) will end the answer display and return to the menu, You may reuse the iast argument entered by pressing ENTER) when asked for the argument. The program wilt display: + and the old argument. You may also use the result of the last computation as the new argument by entering (A) in response to: ARGUMENT? Using the Logarithm Function Call it by entering (2)CS). The program will first ask: ARGUMENT? Answer with the positive number whose logarithms you want. Next it will ask: BASE? Reply with a positive number. The program will then perform the required calculations and display the answer. Example Find log (9). Computer displays: You type: ARGUMENT? (SENTERD BASE? (ENTER (BEEP) 3. Find log (10). Computer displays: You type: ARGUMENT? QM@ENTER) BASE? G@OENTER) (BEEP) 1.430676558 Exponentiation This function allows you to raise any positive number to any power, and a negative number to a positive or integral negative power. First, the program will ask: ARGUMENT? Enter the number you wish to exponentiate. Next, it will ask: EXPONENT? Reply with the power to which you wish to raise the argument. The program will then display the answer. Permissible Numerical Ranges for Functions Entry of an argument for which the function cailed cannot be evaluated will cause the program to beep three times and display: ILLEGAL, then return to the menu. The following list details the numerical range of arguments for which each function is defined: 10 Function Defined Range Undefined Points SIN cos TAN coT SEC csc ASIN ACOS ATAN ACOT ASEC ACSC SINH COSH TANH COTH SECH CSCH ASINH ACOSH ATANH ACOTH ASECH ACSCH No Limits No Limits No Limits No Limits No Limits No Limits ABS(X) < = 1 ABS(X) < = 1 No Limits No Limits ABS(X) > = 1 ABS(X) > = 1 No Limits No Limits No Limits No Limits No Limits No Limits No Limits X>=1 ABS(X) < 1 ABS(X) > 1 0<X<=1 No Limits Within Range None None Pl2 + n*Pl 0, NPI PH2 + n«PI 0, n*PI None None None None None None None None None 0 None 0 None None None None 0 0 Variabie List A—Result Holder B—Argument C—Mode Flag D—Branching Dummy R,S—Sign Flags for Exponentiation VW Appendix A The four Engineering Math packages consist of nine programs designed to handie a variety of algebraic and elementary calculus problems. The contents of the packages are: Package Program Description Engineering GAUSS Gaussian matrix Math | reduction (26-3525) MATMUL Matrix multiplication MATINV Matrix inversion Vector arithmetic Complex arithmetic Advanced trig and exponentials Engineering VECTOR Math II COMPLEX (26-3526) ADVMATH Engineering SIMEQ Linear simultaneous Math Itt equations (26-3527) PCALC Polynomial math and calculus Engineering TRIANG Math IV (26-3528) Solution of triangles 12 The functions of the:programs are as follows: GAUSS—Can complete a Guassian reduction of a square matrix from 3x3 to 10x 10, display the reduced matrix, and calculate its determinant. MATMUL—WIiII multiply an |x J matrix by aU xK matrix, displaying an !x K matrix as the product. lJ +JK must be less than or equal to 108. MATINV—Will catculate the inverse of a square matrix, from 3x3to 6x6. VECTOR—Provides all common vector operations in three dimensions in both Cartesian and polar coordinates: addition, subtraction, dot product, cross product, angle between two vectors, and direct conversion of a vector between rectangular and polar coordinate systems. Chain operations are allowed. The mode may be changed between polar and rectangular at any point during program execution without adversely affecting intermediate results. COMPLEX—Provides for the most common complex number arithmetic operations: addition, subtraction, multiplication, division, calculation of magnitude, conjugation, base-e logarithms, e to complex powers, sines, cosines, arc sines, and arc cosines. Chain operations are allowed. ADVMATH—Provides 24 common trig functions in degree or radian measure. It also provides logarithms to any base and an exponentiation function which can raise negative numbers to positive or integral negative powers. SIMEQ— Solves systems of up to nine linear simultaneous equations for all unknowns. It can also be used to complete a Gaussian reduction of matrices from 2x2 to9x9. PCALC--Provides common polynomial functions and calculus solutions for polynomials to the ninth order. included are: evaluation of the polynomial at any point, calculation of an exact derivative at any point, calculation of an exact integral between any two points, and Newtonian root search. TRIANG—Will solve for the three common unknown triangles (side-side-side, side-angle-side, angle-side- angle) and also can solve from three Cartesian coordinates. TRIANG solves for all sides and angles in any angular unit (degrees, radians, or grads), calculates area, and tests for equilateral, right, Isoscoles, obtuse, and scalene properties. 13 Appendix B—Making a Backup A Backup is a tape copy of a program and is an extremely effective method of insuring that an accident or equiornent fault will not result in the joss of software. Your first action as owner of the Engineering Math Il Package should be to make working copies of the origina! cassette(s) and then put the originals away in a safe place. Although it may be possible to make direct copies using two cassette recorders or on cassetie duplicating equipment, the most reliable method is to use the computer itself to make the Backups. Also, for frequently used programs, you may wish to put them on separate cassettes for easier loading. Here are step-by-step instructions for making a Backup: 1. Cannect the Cassette Interface to the cassette recorder and instali the computer in the Cassette Interface. 2. Place the cassette containing the program(s} to be copied in the recorder and either rewind the tape to the beginning or position the tape to a blank area just prior to the desired program. Piace the recorder in the “Play” mode. It is recommended that the volume control setting be between & and 14 in) 46 on your recorder. if your recorder has a tone control, set it at maximum treble. . Turn on the computer, make sure that it is either in the DEF mode or RUN mode and type in: MO WOXAIDI™) name (7) (name refers to the name of the program to be copied). To make absolutely sure that the program has loaded correctly, use the loading verification procedure as described in the sixth instruction of this appendix. . When the program has been loaded into the computer and the cassette has stopped, remove the cassette and replace it with the cassette which is to receive the program copy. Either rewind the tape to the beginning or position it to the point where the copy is to start. You should leave about ten seconds of blank space if the copy is to follow ancther program on the same cassette. Place the recorder in the “Record” mode. . Make sure that the computer is in either the DEF or RUN mode and type in: CC} SOCAIW EX) name |). The recorder will save your program. . Now rewind the cassette to the blank space just prior to the program, put the recorder into the “Play” mode and type in: COOMBE) name (J. This is the computer’s verifying function. The recorder will start and compare the cassette copy with the program in the computer’s memory. If the copy-is good, the recorder will stop at the end of the program and the prompt sign (>) will reappear on the display. If an error occurred during the verification, the disptay will show an error message such as: 5................. if the error message appears on the display, check the recorder volume setting and try the CLOAD? function once more. If you still get an error, the tape copy is probably damaged. Use the CSAVE function once more and verify the load. It is recommended that you use Radio Shack Supertape or TRS-80 certified cassettes for backing up your Pocket Computer programs. . Backup each program using Steps 1 through 6 above. . Put the original cassettes away in a safe place and use them only for making working copies. 15 - Appendix C—Maintenance Maintenance of your Pocket Computer System is not difficult. Attention to the simplest points listed - below should provide the best feliability and satisfaction: 1. Keep your program cassettes in their boxes when not in use. Do not expose cassettes to temperature extremes or magnetic fields. Never touch the exposed surface of the tape on the front edge of the cassette. 2. Clean: and demagnetize the tape heads in the recorder at regular intervals. Follow the recommendations in the cassette recorder’s manual. 3. The most reliable loading and ‘saving is achieved by ‘operating the cassette recorder on AC current, rather than batteries. 4. Use only fresh alkaline-type batteries in the recorder and Cassette Interface when operating your system away from AC current. 5. Always press the recorder’s “Stop’’ key immediately after loading or saving a program. This will release the pressure on the rubber roller 16 which pulls the tape and prevent the roller from developing a permanent “flat” at the point of contact with the tape. . Always turn the computer “OFF” before installing it in or removing it from the Cassette Interface. . After removing the computer from the Cassette Interface, be sure to reinstall the protective plug to keep dirt out of the connector on the computer. Never touch the exposed parts on the Cassette Interface. RADIO SHACK SOFTWARE LICENSE A. Radio Shack grants to CUSTOMER a non-exclusive. paid up license to use on CUSTOMER'S computer the Radio Shack computer software received. Title to the media: on*which the software is recorded (cassette and/or disk) or stored (ROM) is transferred to the CUSTOMER, but not title to the software. B. In consideration for this license. CUSTOMER shall not reproduce copies of Radio Shack software except to reproduce the number of copies required for use on CUSTOMER'S computer (if the software allows a back- up copy to be made). and shall include Radio Shack’s copyright notice on all copies of software reproduced in whole or in part. C. CUSTOMER may resell Radio Shack's system and applications soit- ware (modified or not. in whole or in part), provided CUSTOMER has purchased one copy of the software for each one resold. The provisions of this software License (paragraphs A. B. and C) shall also be applicable to third parties purchasing such software from CUSTOMER. IMPORTANT NOTICE é ALL RADIO SHACK COMPUTER PROGRAMS ARE LICENSED ON AN “AS IS” BASIS WITHOUT WARRANTY. Radio Shack shall have no liability or responsibility to custonier or any: other person or entity with respect to any liability, loss or damage caused or alleged to be caused directly or indirectly by computer equipment or pro- grams sold by Radio Shack. including but not limited to any interruption of, service, loss of business or anticipatory profits or consequential damages resulting from the use or operation of such cUmputer cz: computer programs.” NOTE: Good data processing procedure dictates that the user test the . program. run and test sample sets of data. and run the system in parallel with the system previously in use for a period of time adequate to insure that results of operation of the | computer or: Program are satisfactory RADIO SHACK Ma DIVISION OF TANDY CORPORATION U.S.A.: FORT WORTH, TEXAS 76102 - CANADA: BARRIE, ONTARIO.L4M 4WS- TANDY CORPORATION } AUSTRALIA eo BELGIUM fxs wk © 280-316 VICTORIAROAD ° PARC INDUSTRIEL OE NANINNE _ BILSTON.AOAD WEDNESBURY RYOALMERE W.S.W. 2116 5140 NANINNE WESFMIOLANOS W510 TN - . 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CUSTOMER is permitted to make additional copies of the Software any for backup or archival purposes or if additional copies are required in the operation of one computer with the Software, but only to the extent the Software aliows a backup copy to be made. However, for TRSDOS Software, CUSTOMER is permitted to make a limited number of additional copies for CUSTOMER’S own use. CUSTOMER may resell or distribute unmodified copies of the Software provided CUSTOMER has.purchased one copy of the Software for each one sold or distributed. The provisions of this Software License shall also be applicable to third parties receiving copies of the Software from CUSTOMER. G. Alt copyright notices shall be retained on all copies of the Software. APPLICABILITY OF WARRANTY A. The terms-and conditions of this Warranty are applicable as between RADIO SHACK and CUSTOMER to either a sale of the Equipment and/or Software License to CUSTOMER or to a transaction whereby RADIO SHACK sells or conveys such Equipment to a third party for jease to CUSTOMER. The limitations of liability and Warranty provisions herein shail inure to the benefit of RADIO SHACK, the author, owner and/or licensor of the Software and any manufacturer of the Equipment sold by RADIO SHACK. STATE LAW RIGHTS The warranties granted herein give the original CUSTOMER specific legal rights, and the original CUSTOMER may have other rights which vary from state to state. 875-9186 a a6. 35 96 ‘ . ‘ Addendum for Engineering Math II (26-3526) Please note the following corrections to the manual: 1. On Page 2, in the list of functions avaitabte in-program VECTOR, the characters “SHFT-" do NOT appear in the program's menu. 2. On page 5, in the list of functions available in program COMPLEX, the eighth line is titled "antilog." When this option is selected, the program will display "E*X." These are different names for the same operation, 3. On Page 9, in the example problem for the logarithm function in program - ADVMATH, the answer is incorrectly shown as 3. The correct answer to the sample problem is 2. ; H -Aive 79 From A=W (G+s9e(s8)) To =LM(B+S9ex(g8-2)) 875-9188