Practical Use of Mathcad Solving Mathematical Problems with a Computer Algebra System
| Title |
|---|
| Practical Use of Mathcad Solving Mathematical Problems with a Computer Algebra System |
| Number of Page |
| 518 page |
| File Type |
| File Size |
| 22 MB |
1 Introduction ... 1
1.1 Structure and Operation of Computer Algebra Systems ... 2
1.2 Application Areas for Computer Algebra Systems .... 6
1.3 Development of MATHCAD ... 11
1.4 Comparison of MATHCAD with other Systems ... 13
2 Installation of MathCAD ... 14
2.1 Program Installation ... 14
2.2 MATHCAD Files .... 15
2.3 Help System .... 16
2.4 AXUM ....... 18
3 MathCAD User Interface ... 20
3.1 Menu Bar ......... 21
3.2 Standard Toolbar ...... 23
3.3 Formatting Toolbar .... 24
3.4 Math Toolbar ... 24
3.5 Worksheet .... 29
3.6 Status Bar ..... 31
4 MathCAD Worksheet .... 32
4.1 Text Arrangement. ..... 36
4.2 Layout of Calculations ... 38
4.3 Worksheets Management. .. .40
5 Electronic Books 44
5.1 Properties, Structure and Handling ...... .45
5.2 Books Available, Extension Packs and Libraries . .50
6 Exact and Numerical Calculations .... 54
6.1 Exact Calculation Using Computer Algebra .......... 57
6.2 Numerical Calculations ............ 64
6.3 Control of the Calculation ........ 66
6.4 Error Messages ..... 71
7 Numbers ..... 72
7.1 Real Numbers ...... 73
7.2 Complex Numbers ..... 74
7.3 Built-in Constants 77
8 V ariables ..... 79
8.1 Built-In Variables . 79
8.2 Simple and Indexed Variables .... 80
8.3 Range Variables ... 82
8.4 Strings .... 87
9 Data.Management. .... 89
9.1 Data Input ............ 91
9.2 Data Output ......... 97
9.3 Data Exchange ... 101
10 Programming ......... 102
10.1 Boolean Operators and Logical Operators .... 104
10.2 Defmition of Operators ............. 105
10.3 Assignments ....... 108
10.4 Branches ............ 109
10.5 Loops ... 111
10.6 Programming Examples ............. 118
11 Dimensions and Units of Measure .....• 129
12 Basic Arithmetic Operations ........ 133
13 Transformadon of Expressions ... 135
13.1 Introduction ....... 135
13.2 Simplification ..... 138
13.3 Partial Fraction Decomposition . 139
13.4 Expansion .......... 140
13.5 Multiplication ..... 142
13.6 Factorization ...... 143
13.7 Reduce to a Common Denominator .............. 145
13.8 Substitution ........ 145
13.9 Transformation of Trigonometric Expressions ............... 146
14 Sums atld Products ..... , 149
15 vectors atld MaUices ... 154
15.1 Input .... 155
15.2 Vector and Matrix Functions ..... 164
15.3 Computational Operations ..... 167
15.4 Determinants ............ 178
15.5 Eigenvalues and Eigenvectors 181
16 Equations and Inequalities ........ 185
16.1 Systems of linear Equations and Analytical Geometry ........ 185
16.2 Polynomials ... 196
16.3 Nonlinear Equations ..... 203
16.4 Numerical Solution Methods .. 211
16.5 Inequalities .... 219
17 Functions .... 224
17.1 General Functions .................. 225
17.2 Mathematical Functions .......... 232
18 Gra.phics Features ..... 249
18.1 Curves ........... 249
18.2 Surfaces .......... 264
18.3 Scatter Plots .... 274
18.4 Diagrams ........ 280
18.5 Animations ..... 282
18.6 Import and Export of Graphics .............. 285
19 Differentiation .... 286
19.1 Calculation of Derivatives ...... 286
19.2 Taylor Expansion .................... 295
19.3 Calculus of Errors ................... 301
19.4 Calculation of Limits ............... 303
19.5 Discussion of Curves .............. 307
20 Integt-a.don ..... 315
20.1 Indefmite Integrals ................. 315
20.2 Defmite Integrals .................... 322
20.3 Improper Integrals .................. 325
20.4 Numerical Methods ................. 329
20.5 Multiple Integrals .................... 335
21 Inftni'te Series an.d Products ...... 338
21.1 Number Series and Products .. 338
21.2 Power Series .. 343
21.3 Fourier Series .. 344
Vector Analysis ... 348
22.1 Fields and their Graphical Display .... 348
22.2 Gradient, Rotation and Divergence ... 352
22.3 Curvilinear and Surface Integrals ....... 356
23 Differential Equations ... 358
23.1 Ordinary Differential Equations ......... 358
23.2 Partial Differential Equations ............. 379
24 Transformations ... 383
24.1 Laplace Transfonnation ... 383
24.2 Fourier Transfonnation ... 387
24.3 Z-Transfonnation ....... 388
24.4 Wavelet Transfonnation ... 391
24.5 Solution of Difference and Differential Equations ... 393
25 Optimization....... 401
25.1 Extreme Value Problems ...402
25.2 Linear Programming ..... 410
25.3 Nonlinear Programming .... 416
25.4 Numerical Methods .... 418
26 Probability... 431
26.1 Combinatorics ... 432
26.2 Probability and Random Variables ... .434
26.3 Expected Value and Variance ........... .437
26.4 Distribution Functions ..... 438
26.5 Random Numbers ........ 447
27 Statistics..... 45 1
27.1 Parameters of a Sample ...... 453
27.2 Correlation and Regression .... .460
27.3 Simulations ...... 472
27.4 Electronic Books for Statistics ........... .476
28 Summary... 487
Bibliography ............ 490
Index......................... 493
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