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Preface | p. xiii |
List of Figures | p. xv |
An Introduction to Matlab® | p. 1 |
The Matlab Software Package | p. 1 |
Matrices and Matrix Operations in Matlab | p. 3 |
Manipulating the Elements of a Matrix | p. 5 |
Transposing Matrices | p. 8 |
Special Matrices | p. 9 |
Generating Matrices and Vectors with Specified Element Values | p. 10 |
Matrix Functions | p. 13 |
Using the Matlab \ Operator for Matrix Division | p. 14 |
Element-by-Element Operations | p. 14 |
Scalar Operations and Functions | p. 15 |
String Variables | p. 19 |
Input and Output in Matlab | p. 24 |
Matlab Graphics | p. 27 |
Three-Dimensional Graphics | p. 34 |
Manipulating Graphics-Handle Graphics | p. 35 |
Scripting in Matlab | p. 43 |
User-Defined Functions in Matlab | p. 49 |
Data Structures in Matlab | p. 53 |
Editing Matlab Scripts | p. 57 |
Some Pitfalls in Matlab | p. 59 |
Faster Calculations in Matlab | p. 60 |
Problems | p. 61 |
Linear Equations and Eigensystems | p. 67 |
Introduction | p. 67 |
linear Equation Systems | p. 70 |
Operators \ and / for Solving Ax = b | p. 75 |
Accuracy of Solutions and Ill-Conditioning | p. 80 |
Elementary Row Operations | p. 83 |
Solution of Ax = b by Gaussian Elimination | p. 84 |
LU Decomposition | p. 86 |
Cholesky Decomposition | p. 91 |
QR Decomposition | p. 93 |
Singular Value Decomposition | p. 97 |
The Pseudo-Inverse | p. 100 |
Over- and Underdetermined Systems | p. 106 |
Iterative Methods | p. 114 |
Sparse Matrices | p. 115 |
The Eigenvalue Problem | p. 126 |
Iterative Methods for Solving the Eigenvalue Problem | p. 130 |
The Matlab Function eig | p. 135 |
Summary | p. 139 |
Problems | p. 140 |
Solution of Nonlinear Equations | p. 147 |
Introduction | p. 147 |
The Nature of Solutions to Nonlinear Equations | p. 149 |
The Bisection Algorithm | p. 150 |
Iterative or Fixed Point Methods | p. 151 |
The Convergence of Iterative Methods | p. 152 |
Ranges for Convergence and Chaotic Behavior | p. 153 |
Newton's Method | p. 156 |
Schroder's Method | p. 160 |
Numerical Problems | p. 162 |
The Matlab Function fzero and Comparative Studies | p. 164 |
Methods for Finding All the Roots of a Polynomial | p. 166 |
Solving Systems of Nonlinear Equations | p. 171 |
Broyden's Method for Solving Nonlinear Equations | p. 175 |
Comparing the Newton and Broyden Methods | p. 178 |
Summary | p. 178 |
Problems | p. 179 |
Differentiation and Integration | p. 185 |
Introduction | p. 185 |
Numerical Differentiation | p. 185 |
Numerical Integration | p. 189 |
Simpson's Rule | p. 190 |
Newton-Cotes Formulae | p. 194 |
Romberg Integration | p. 196 |
Gaussian Integration | p. 198 |
Infinite Ranges of Integration | p. 201 |
Gauss-Chebyshev Formula | p. 206 |
Gauss-Lobatto Integration | p. 207 |
Filon's Sine and Cosine Formulae | p. 211 |
Problems in the Evaluation of Integrals | p. 215 |
Test Integrals | p. 217 |
Repeated Integrals | p. 219 |
Matlab Functions for Double and Triple Integration | p. 224 |
Summary | p. 225 |
Problems | p. 226 |
Solution of Differential Equations | p. 233 |
Introduction | p. 233 |
Euler's Method | p. 235 |
The Problem of Stability | p. 237 |
The Trapezoidal Method | p. 239 |
Runge-Kutta Methods | p. 242 |
Predictor-Corrector Methods | p. 246 |
Hamming's Method and the Use of Error Estimates | p. 249 |
Error Propagation in Differential Equations | p. 251 |
The Stability of Particular Numerical Methods | p. 252 |
Systems of Simultaneous Differential Equations | p. 256 |
The Lorenz Equations | p. 259 |
The Predator-Prey Problem | p. 260 |
Differential Equations Applied to Neural Networks | p. 262 |
Higher-Order Differential Equations | p. 266 |
Stiff Equations | p. 267 |
Special Techniques | p. 270 |
Extrapolation Techniques | p. 274 |
Summary | p. 276 |
Problems | p. 276 |
Boundary Value Problems | p. 283 |
Classification of Second-Order Partial Differential Equations | p. 283 |
The Shooting Method | p. 284 |
The Finite Difference Method | p. 287 |
Two-Point Boundary Value Problems | p. 289 |
Parabolic Partial Differential Equations | p. 295 |
Hyperbolic Partial Differential Equations | p. 299 |
Elliptic Partial Differential Equations | p. 302 |
Summary | p. 309 |
Problems | p. 310 |
Fitting Functions to Data | p. 313 |
Introduction | p. 313 |
Interpolation Using Polynomials | p. 313 |
Interpolation Using Splines | p. 317 |
Fourier Analysis of Discrete Data | p. 321 |
Multiple Regression: Least Squares Criterion | p. 335 |
Diagnostics for Model Improvement | p. 339 |
Analysis of Residuals | p. 343 |
Polynomial Regression | p. 347 |
Fitting General Functions to Data | p. 355 |
Nonlinear Least Squares Regression | p. 356 |
Transforming Data | p. 359 |
Summary | p. 363 |
Problems | p. 363 |
Optimization Methods | p. 371 |
Introduction | p. 371 |
Linear Programming Problems | p. 371 |
Optimizing Single-Variable Functions | p. 378 |
The Conjugate Gradient Method | p. 382 |
Moller's Scaled Conjugate Gradient Method | p. 388 |
Conjugate Gradient Method for Solving Linear Systems | p. 394 |
Genetic Algorithms | p. 397 |
Continuous Genetic Algorithm | p. 413 |
Simulated Annealing | p. 418 |
Constrained Nonlinear Optimization | p. 421 |
The Sequential Unconstrained Minimization Technique | p. 426 |
Summary | p. 429 |
Problems | p. 429 |
Applications of the Symbolic Toolbox | p. 433 |
Introduction to the Symbolic Toolbox | p. 433 |
Symbolic Variables and Expressions | p. 434 |
Variable-Precision Arithmetic in Symbolic Calculations | p. 439 |
Series Expansion and Summation | p. 441 |
Manipulation of Symbolic Matrices | p. 444 |
Symbolic Methods for the Solution of Equations | p. 449 |
Special Functions | p. 450 |
Symbolic Differentiation | p. 452 |
Symbolic Partial Differentiation | p. 454 |
Symbolic Integration | p. 456 |
Symbolic Solution of Ordinary Differential Equations | p. 459 |
The Laplace Transform | p. 464 |
The Z-Transform | p. 466 |
Fourier Transform Methods | p. 468 |
Linking Symbolic and Numerical Processes | p. 472 |
Summary | p. 475 |
Problems | p. 475 |
Appendices | |
Matrix Algebra | p. 481 |
Introduction | p. 481 |
Matrices and Vectors | p. 481 |
Some Special Matrices | p. 482 |
Determinants | p. 483 |
Matrix Operations | p. 484 |
Complex Matrices | p. 485 |
Matrix Properties | p. 486 |
Some Matrix Relationships | p. 486 |
Eigenvalues | p. 487 |
Definition of Norms | p. 487 |
Reduced Row Echelon Form | p. 488 |
Differentiating Matrices | p. 489 |
Square Root of a Matrix | p. 490 |
Error Analysis | p. 491 |
Introduction | p. 491 |
Errors in Arithmetic Operations | p. 492 |
Errors in the Solution of Linear Equation Systems | p. 493 |
Solutions to Selected Problems | p. 497 |
Bibliography | p. 521 |
Index | p. 525 |
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