The Business Master (3rd Edition)

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SCICALC Math Utilities Demo Scicalc 2.0 Bob Zorich Acro Technology, Inc. 1111 W El Camino Real Suite 331 Sunnyvale, CA 94086 Copyright 1985, 1986 Acro Technology All Rights Reserved This file is the description for the Scicalc Math Utilities demo program. This is a totally rewritten version of the Scicalc Math Demo Version 1.0, released in August, 1985, and version 1.2, released February, 1986. The SCICALC Math Utilities Demo program is hereby released to the Public Domain using the concept of "Shareware". Share this program with your friends, user's groups, and your favorite BBS. Please do not modify the program in any way, or try to accept remuneration for it. After all, MANY hours of work were put into this work, the authors should get the credit. Treat it the same as you would expect OTHERS to treat YOUR work. If you feel that this program has benefited you, then please find it in your heart to send $20.00 to the above address. The demo program illustrates the use of, and finds accurate solutions to over 250 functions. These functions range from unit conversions to Fast Fourier Transform, Complex Number analysis, matrix algebra, and a wide variety of others. A complete list of the functions available is at the end of this file. NOTICE : To move up one level or to cancel the window you are in type "0". This program is set up to run in a completely windowed mode, at some point in the future, I may make it memory resident. Right now, it runs only as a stand alone program. This version is also not compiled for use of the 8087 coprocessor, although a version exists that does use 8087's. I am attemping to reach the widest possible number of users with this version. The Scicalc Demo program was developed on an IBM XT, and has been tested on an IBM AT with Hercules graphics. It requires 192K of free RAM, of which about 40K is used for window storage, and 40-45K bytes are for program space. The rest of the space is reserved for heap space, which is where all matrix manipulations are done. The program also expects the use of IBM's CGA, although it only uses Text Mode and should therefore be compatible with almost everything, except the monochrome adaptor, which may give some trouble. In general, the routines are error protected, especially against illegal input. However, there may still be conditions that will cause the program to dump. There are limitations to what you can do, such as the size of three dimensional matrices. These limitations will be described in a minute. The program is fairly self-explanatory, with all functions called through menus, and most input routines labelled for what is expected. There is no direct on-line help, but short of putting in gibberish into the routines, the program will "lead" you through. The solutions are sometimes returned as real numbers, sometimes as complex numbers, sometimes as vectors. Again, it should be relatively clear as to what is being displayed. The basic limitations are these: 1- Matrices have limited size capabilities, limited due to the methods I have used implementing the window routines. The math routines themselves are only limited by the available memory. The maximum sizes are about 20 items in a one dimensional vector, about an 8x8 two dimensional matrix, and about 4x4x3 three dimensional matrix. 2- Second and third level menus may crash if the value entered to select the menu choice does not exist on the menu. This is not a serious issue, as long as you are careful with data entry. 3- Needs 192K RAM, Color Graphics Adaptor, one disk drive (preferably a hard drive), MS-DOS 2.1 or higher. Known to be incompatible with IBM Monochrome Graphics Board. 4- Non-8087 version limited to real values under abs(1e37). This can only be noticed in very unusual circumstances, and in most cases, this number will not be exceeded. Watch out for intermediate solutions exceeding these limits. The Math Utilities and all source code of these routines are available from Acro Technology, Inc. The source codes for the math routines are written in Turbo Pascal and are built so that all variables are passed on the command line, and so that only stack and heap space are used. The actual data segment size on the math routines themseleves is 32 bytes. They are commented, and written in an easy to use modular manner. All error trapping is already built in, any user extensions to the error trapping routines are easy to implement. Use of the routines is as easy as including the modules that you need, and then interfacing the functions to your programs. The following is a list of all math functions available within the Scicalc Math Utilities Package: NOTICE : To move up one level or to cancel the window you are in type "0". Function Evaluations Solutions to Common Formulas ---------------------------- 1- Polynomial Evaluations 2- Quadratic Formula 3- Newton Raphson Roots 4- Derivative Calculation 5- Function Integration 6- Integration by Data 7- Gaussian Elimination 8- Fast Fourier Transform Statistical Tables Various Statistical Formulas ---------------------------- 1- Geometric Mean of List 2- Arithmetic Mean List 3- Median of a List 4- Variance of a List 5- Standard Deviation 6- Binomial Distribution 7- Poisson Distribution 8- Normal Distribution General Math Functions Solutions to Common Formulas ---------------------------- 1- Log Base 10 2- Log Any Base 3- Factorial 4- Nth Power of Real 5- Nth Root of Real 6- Permutations 7- Combinations 8- Max Min Locator 9- Find Circle 3 Pts 10- Gaussian Dist Random # 11- Sieve Eratosthenes 12- Great Common Denom Complex Algebra Common Complex Number Functions ------------------------------- 1- Real to Complex 2- Complex to Polar 3- Polar to Complex 4- Complex Conjugate 5- Multiply by Scalar 6- Addition 7- Add N Complex 8- Subtraction 9- Multiplication 10- Division 11- Raise to Real 12- Complex Root 13- Complex Exponential 14- Complex Sine 15- Complex Cosine 16- Complex Tangent 17- Complex Square 18- Complex Square Root 19- Complex Natural Log 20- Raise to Complex Physical Phenomena General and Relativistic Functions ---------------------------------- 1- Angular Momentum 2- Percent C to Met/sec 3- Meter/Sec to Percent C 4- Rel Distortion 5- Lorentz Transform 6- Velocity Addition 7- Velocity Add Prime 8- Time Distortion 9- Mass Distortion 10- Rel Kinetic Energy 11- Rel Total Energy 12- Rel Momentum 13- Radius of Particle Moving in Magnetic Field Co-ordinate System Transformation --------------------------------- 1- Rectang to Polar 2- Polar to Rectang 3- Spherical to Rectang 4- Rectang to Spher 5- Cylin to Rectang 6- Rectang to Cylind 7- Translate and Rotate 8- Scale Factor Trigonometric Functions Extended Trig Functions ----------------------- 1- Degrees to Radians 3- Tangent 5- Secant 2- Radians to Degrees 4- Cosecant 6- Cotangent Arc Trig Functions ------------------ 1- Arc Sine 3- Arc Cotangent 5- Arc Secant 2- Arc Cosine 4- Arc Cosecnt Hyperbolic Functions -------------------- 1- Hyperbolic Sine 3- Hyperbolic Tangent 5- Hyperbolic Secant 2- Hyperbolic Cosine 4- Hyperbolic Cosecant 6- Hyperbolic Cosecant Arc Hyperbolic Functions ------------------------ 1- Arc Hyperbolic Sine 4- Arc Hyper Tangent 7- Arc Hyp Secant 2- Arc Hyperbolic Cosine 5- Arc Hyper Cotangent 8- Alt Arc Hyper Secant 3- Alt Arc Hyper Cosine 6- Arc Hyper Cosecant Mensuration Tables 2-d Figures ----------- 1- Circumference of Circle 2- Area of Circle 3- Circumference of Ellipse 4- Area of Ellipse Cubes ----- 1- Volume of Box 2- Area of Box 3- Diagonal of Box 4- Diagonal of Face Cylinders --------- 1- Surface Area of Sid of Cylinder 2- Total Surface Area of Cylinder 3- Volume of Cylinder Cones / Conic Sections ---------------------- 1- Volume of general right cone 2- Slant height of side 3- Area of side of cone 4- Total Area of cone 5- Volume of cone 6- Side Area of Frustrum 7- Total Area of Frustrum 8- Volume of Frustrum Spheres / Spherical Sections ---------------------------- 1- Surface Area of Sphere 2- Volume of Sphere 3- Area of one zone of Sphere 4- Volume of one zone of sphere 5- Area of two zones of Sphere 6- Volume of two zones of sphere Spheroids / Ellipsoidal Solids ------------------------------ 1- Surface Area of Lune 2- Eccentricity of Ellipse 3- Sur Area of Oblate Ellipsoid 4- Volume of Oblate Spheroid 5- Sur Area of Prolate Ellipsoid 6- Volume of Prolate Spheroid 7- Surface area of Torus 8- Volume of Torus Matrix Functions Matrix Primitives ----------------- 1- Null Vector 2- 2-d Null Matrix 3- 3-d Null Matrix 4- 2-d Unit Matrix 5- Copy Vector 6- Copy 2-d Matrix 7- Copy 3-d Matrix 8- Swap Rows 2-d Mat 9- Swap Columns 2-d Matrix 10- Insert Row 2-d Mat 11- Insert Column 2-d 12- Delete Column 13- Delete Row 14- Send Row to Vector 15- Send Column to Vector 16- Send Diagonal to Vec 17- Send Vector to Row 18- Send Vector to column 19- Send Vector to Diag Matrix Evaluations ------------------ 1- Magnitude of a vector 2- Dot Product 3- Angle Between Vectors 4- Cross Product 5- Add Two Vectors 6- Add N Vectors 7- Add and Subtract Mat 8- Matrix Multiply 9- Transpose Matrix 10- Multiply by Scalar 11- Invert Matrix 12- Multiply by inverse 13- Add Constant to Matrix 14- 3-d Add / Subtract 15- 3-d Matrix Mult 16- 3-d Scalar Multiply Matrix Functions ---------------- 1- Square Vector 2- Square 2-d Matrix 3- Square 3-d Matrix 4- Square Root Vector 5- Square Root 2-d Mat 6- Sqare root 3-d matrix 7- Absolute Value Vector 8- Absolute 2-d Matrix 9- Absolute 3-d Matrix 10- Round Vector 11- Round 2-d Matrix 12- Round 3-d Matrix 13- Truncate Vector 14- Truncate 2-d matrix 15- Truncate 3-d Matrix 16- Natural Log Vector 17- Ln of 2-d matrix 18- Ln of 3-d matrix 19- Exponential vector 20- Exponential 2-d Mat 21- Exponential 3-d Mat Unit Conversion Functions Linear ------ 1- Cm to Inch 9- Yards to Meters 17- Feet to Fathom 2- Meters to Feet 10- Miles to Km 18- Fathom to Feet 3- Meters to Yards 11- Mile to Feet 19- Light Year to Meter 4- Km to Miles 12- Feet to Mile 20- Meter to Light Year 5- Millimeter to Micron 13- Naut Mile to Mile 21- Light Year to Parsec 6- Micron to Millimeter 14- Mile to Naut Mile 22- Parsec to Light Year 7- Inch to CM 15- Angstrom to Meter 8- Feet to Meters 16- Meter to Angstrom Spatial ------- 1- Sq Meter to Sq Foot 7- Acres to Sq Foot 13- Cub Inch to Cub Meter 2- Sq Inch to Sq Meter 8- Sq Foot to Acres 14- Cub Meter to Cub Inch 3- Cub Meter to Cub Foot 9- Acre to Hectare 15- Cub Foot to Cub Inch 4- Cub Foot to Cub Meter 10- Hectare to Acre 16- Cub Inch to Cub Foot 5- Sq Foot to Sq Meter 11- Acre to Sq Mile 6- Sq Meter to Sq Foot 12- Sq Mile to Acre Mass/Density ------------ 1- Gram to Ounce 7- Ton to Pound 13- Kg/Cub M to Gm/Cub Cm 2- Kilogram to Pound 8- Pound to Ton 14- Gm/Cub Cm to Kg/Cub M 3- Ounce to Gram 9- KGram/Cub Met to Lb/Cub Foot 4- Pound to Kilogram 10- Lb/Cub Foot to KGram/Cub Met 5- AMU to Gram 11- Gm/Cub Inch to Lb/Cub Cm 6- Gram to Amu 12- Lb/Cub Inch to Gm/Cub Cm Fluids ------ 1- Liter to Gallon 5- Gallon to Cub Inch 9- Fluid Ounce to Gallon 2- Fl Oz to Milliliter 6- Cub Inch to gallon 10- Gallon to Fl. Ounce 3- Millilliter to Fl Oz 7- Liter to Cub Meter 4- Gallon to Liter 8- Cub Meter to Liter Time ---- 1- Year to Day 5- Day to hour 9- Hour to Minute 2- Day to Year 6- Hour to Day 10- Minute to Hour 3- Year to Second 7- Hour to Second 4- Second to Year 8- Second to Hour Energy ------ 1- Joules to BTU 5- Joules to Ft-Lb 9- Dyne to Newton 2- BTU to Joules 6- Ft-Lb to Joules 10- BTU to Calories 3- HP to Kwatts 7- BTU/Min to Watts 11- Calories to BTU 4- Kwatts to HP 8- Newton to Dyne Velocity -------- 1- MPH to Knots 3- KM/Hr to Mile/Hr 5- Mile/Hr to Feet/Sec 2- Knots to MPH 4- Mile/Hr to KM/Hour 6- Feet/sec to Mile/Hr Pressure -------- 1- PSI to Atmosphere 4- MmHg to Atmosphere 7- MlBar to Dyne/cm 2- Atmosphere to PSI 5- PSI to Dyne/CM 8- Dyne/Cm to MlBar 3- Atmos to MmHg 6- Dyne/Cm to PSI Temperature ----------- 1- Celsius to Fahrenheit 3- Kelvin to Fahrenheit 5- Kelvin to Celsius 2- Fahrenheit to Celsius 4- Fahrenheit to Kelvin 6- Celsius to Kelvin NOTICE : To move up one level or to cancel the window you are in type "0".