12.Computational Science and Engineering

Gilbert Strang9780961408817, 0961408812

This book presents the full range of computational science and engineering — the equations, numerical methods, and algorithms with MATLAB® codes. The author has taught this material to thousands of engineers and scientists. The book is solution-based and not formula-based: it covers applied linear algebra and fast solvers, differential equations with finite differences and finite elements, Fourier analysis, optimization, and more.
Contents Chapter 1: Applied Linear Algebra; Chapter 2: A Framework for Applied Mathematics; Chapter 3: Boundary Value Problems; Chapter 4: Fourier Series and Integrals; Chapter 5: Analytic Functions; Chapter 6: Initial Value Problems; Chapter 7: Solving Large Systems; Chapter 8: Optimization and Minimum Principles.

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Table of contents :
Local Disk……Page 0
12• Computational Science and Engineering……Page 1
Abstract……Page 4
Algorithmic Differentiation and Differencing……Page 6
Abstract……Page 17
Bessel Functions……Page 18
Abstract……Page 25
Boundary-Value Problems……Page 27
Abstract……Page 43
Calculus……Page 45
Abstract……Page 59
Chaotic Systems Control……Page 61
Abstract……Page 79
Abstract……Page 81
Convolution……Page 83
Abstract……Page 100
Correlation Theory……Page 102
Abstract……Page 117
Describing Functions……Page 119
Abstract……Page 154
Duality, Mathematics……Page 156
Abstract……Page 166
Eigenvalues and Eigenfunctions……Page 168
Abstract……Page 181
Elliptic Equations, Parallel Over Successive Relaxation Algorithm……Page 183
Abstract……Page 191
Equation Manipulation……Page 193
Abstract……Page 237
Fourier Analysis……Page 239
Abstract……Page 251
Function Approximation……Page 253
Abstract……Page 262
Gaussian Filtered Representations of Images……Page 264
Abstract……Page 284
Geometry……Page 286
Abstract……Page 291
Graph Theory……Page 293
Abstract……Page 303
Green’s Function Methods……Page 305
Abstract……Page 320
Hadamard Transforms……Page 322
Abstract……Page 336
Hankel Transforms……Page 338
Abstract……Page 357
Hartley Transforms……Page 359
Abstract……Page 369
Hilbert Spaces……Page 371
Abstract……Page 389
Abstract……Page 391
Homotopy Algorithm for Riccati Equations……Page 393
Abstract……Page 418
Horn Clauses……Page 420
Abstract……Page 433
Integral Equations……Page 435
Abstract……Page 446
Integro-Differential Equations……Page 448
Abstract……Page 458
Laplace Transforms……Page 460
Abstract……Page 469
Least-Squares Approximations……Page 471
Abstract……Page 493
Linear Algebra……Page 495
Abstract……Page 508
Lyapunov Methods……Page 510
Abstract……Page 521
Minimization……Page 523
Abstract……Page 527
Minmax Techniques……Page 529
Abstract……Page 545
Nomograms……Page 547
Abstract……Page 554
Nonlinear Equations……Page 556
Abstract……Page 565
Number Theory……Page 567
Abstract……Page 586
Ordinary Differential Equations……Page 588
Abstract……Page 613
Polynomials……Page 615
Abstract……Page 628
Probabilistic Logic……Page 629
Abstract……Page 639
Probability……Page 641
Abstract……Page 654
Process Algebra……Page 656
Abstract……Page 681
Random Matrices……Page 683
Abstract……Page 708
Roundoff Errors……Page 710
Abstract……Page 721
Switching Functions……Page 723
Abstract……Page 730
Temporal Logic……Page 732
Abstract……Page 741
Theory of Difference Sets……Page 743
Abstract……Page 756
Time-Domain Analysis……Page 758
Abstract……Page 780
Transfer Functions……Page 782
Abstract……Page 794
Traveling Salesperson Problems……Page 796
Abstract……Page 811
Vectors……Page 813
Abstract……Page 821
Walsh Functions……Page 823
Abstract……Page 835
Wavelet Methods for Solving Integral and Differential Equations……Page 837
Abstract……Page 848
Wavelet Transforms……Page 850
Abstract……Page 870
Z Transforms……Page 872