Practical Use of MathcadŽ: Solving Mathematical Problems With a Computer Algebra System

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Springer Science & Business Media, Oct 15, 1999 - Computers - 505 pages
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This book, which is a rrMsion and extension of the original edition publi shed in 1996 (see [2D with the German title Mathematik mit MA'nfCAD (Mathematics Using MA'nfCAD), discusses the use of the program system MAlHCADŽ to solve mathematical problems with computers. The book is based on the current MA'nfCAD Version 8 Professional for WINDOWS 95/98 (see [5D. Whereas MAlHCAD and MATLAB (see [4D were originally conceived as purely systems for numerical mathematical calculations, the more recent versions of both products have licensed a minimum variant of the symbolic processor of the MAPLE computer algebra system for exact (symbolic) calcu lations. Thus, MAlHCAD has been developed to be an equal partner to the estab lished computer algebra systems AXIOM, DERIVE, MACSYMA, MAPLE, MA lHEMATICA, MuPAD and REDUCE. However, because these systems con tain numerical methods as well, they are no longer just pure computer alge bra systems. Consequently, MAlHCAD can also be deSignated as being a computer alge bra system (or just: system). MATHCAD possesses some advantages: • Better numerical capabilities more than compensate for the somewhat limited capabilities provided for exact (symbolic) calculations. • The calculations are performed in the MAlHCAD worksheet using the usual mathematical symbols (standard notation). • Thanks to the superior layout capabilities in the worksheet, MAlHCAD can be used to create treatises directly. • All calculations can be performed using units of measurement.
 

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Contents

Introduction
1
11 Structure and Operation of Computer Algebra Systems
2
12 Application Areas for Computer Algebra Systems
6
13 Development of MATHCAD
11
14 Comparison of MATHCAD with other Systems
13
Installation of MATHCAD
14
22 MATHCAD Files
15
23 Help System
16
1532 Transposition
173
1533 Inverse
174
1534 Scalar Vector and Scalar Triple Product
176
154 Determinants
178
155 Eigenvalues and Eigenvectors
181
Equations and Inequalities
185
162 Polynomials
196
163 Nonlinear Equations
203

24 AXUM
18
MATHCAD User Interface
20
31 Menu Bar
21
32 Standard Toolbar
23
33 Formatting Toolbar
24
35 Worksheet
29
36 Status Bar
31
MATHCAD Worksheet
32
41 Text Arrangement
36
42 Layout of Calculations
38
43 Worksheets Management
40
432 Layout
41
434 Insertion of Objects
43
Electronic Books
44
51 Properties Structure and Handling
45
52 Books Available Extension Packs and Libraries
50
Exact and Numerical Calculations
54
61 Exact Calculation Using Computer Algebra
57
611 Symbolic Equal Sign
58
612 Keywords
61
62 Numerical Calculations
64
63 Control of the Calculation
66
631 Automatic Mode
67
633 Termination of Calculations
68
635 Optimization
69
64 Error Messages
71
Numbers
72
71 Real Numbers
73
72 Complex Numbers
74
73 Builtin Constants
77
Variables
79
82 Simple and Indexed Variables
80
83 Range Variables
82
84 Strings
87
Data Management
89
91 Data Input
91
92 Data Output
97
93 Data Exchange
101
Programming
102
101 Boolean Operators and Logical Operators
104
102 Definition of Operators
105
103 Assignments
108
104 Branches
109
105 Loops
111
106 Programming Examples
118
1061 Error Handling
119
1062 Examples
120
Dimensions and Units of Measure
129
Basic Arithmetic Operations
133
Transformation of Expressions
135
132 Simplification
138
133 Partial Fraction Decomposition
139
134 Expansion
140
135 Multiplication
142
136 Factorization
143
137 Reduce to a Common Denominator
145
139 Transformation of Trigonometric Expressions
146
Sums and Products
149
Vectors and Matrices
154
151 Input
155
1511 Input of Vectors
156
1512 Input of Matrices
160
152 Vector and Matrix Functions
164
153 Computational Operations
167
1531 Addition and Multiplication
171
164 Numerical Solution Methods
211
165 Inequalities
219
Functions
224
171 General Functions
225
1712 Sorting Functions
226
1713 String Functions
231
172 Mathematical Functions
232
1721 Elementary Functions
233
1722 Special Functions
235
1724 Approximation of Functions
242
Graphics Features
249
182 Surfaces
264
183 Scatter Plots
274
184 Diagrams
280
185 Animations
282
186 Import and Export of Graphics
285
Differentiation
286
192 Taylor Expansion
295
193 Calculus of Errors
301
194 Calculation of Limits
303
195 Discussion of Curves
307
Integration
315
202 Definite Integrals
322
203 Improper Integrals
325
204 Numerical Methods
329
205 Multiple Integrals
335
Infinite Series and Products
338
212 Power Series
343
213 Fourier Series
344
Vector Analysis
348
222 Gradient Rotation and Divergence
352
223 Curvilinear and Surface Integrals
356
Differential Equations
358
2311 Initial Value Problems
359
2312 Boundary Value Problems
373
232 Partial Differential Equations
379
Transformations
383
242 Fourier Transformation
387
243 ZTransformation
388
244 Wavelet Transformation
391
245 Solution of Difference and Differential Equations
393
Optimization
401
251 Extreme Value Problems
402
252 Linear Programming
410
253 Nonlinear Programming
416
254 Numerical Methods
418
Probability
431
261 Combinatorics
432
262 Probability and Random Variables
434
263 Expected Value and Variance
437
264 Distribution Functions
438
265 Random Numbers
447
Statistics
451
271 Parameters of a Sample
453
272 Correlation and Regression
460
2721 Introduction
461
2722 Linear Regression Curves
462
2723 Nonlinear Regression Curves
465
273 Simulations
472
274 Electronic Books for Statistics
476
Summary
487
Bibliography
490
Index
493
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