| 作 者： | John Mathews Kurtis Fink |
| 出版社： | 电子工业出版社 |
| 丛编项： | 国外计算机科学教材系列 |
| 版权说明： | 本书为公共版权或经版权方授权，请支持正版图书 |
| 标 签： | Matlab |
| ISBN | 出版时间 | 包装 | 开本 | 页数 | 字数 |
|---|---|---|---|---|---|
| 未知 | 暂无 | 暂无 | 未知 | 0 | 暂无 |
1 Preliminaries 1
1.1 Review of Calculus 2
1.2 Binary Numbers I3
1.3 Error Analysis 24
2 The Solution of Nonlinear Equations
f(x) == 0 40
2.l Iteration for Solving x = g(x) 41
2.2 Bracketing Methods for Locating a Root 51
2.3 Initial Approximation and Convergence Criteria 62
2.4 Newton-Raphson and Secant Methods 70
2.5 Aitken's Process and Steffensen's and
Muller's Methods (Optional) 90
3 The Solution of Linear Systems AX = B
3.1 Introduction to Vectors and Matrices 101
3.2 Properties of Vectors and Matrices 109
3.3 Uppertriangular Linear Systems i20
3.4 Gaussian Elimination and Pivoting 125
3.5 TriangularFactorization 141
3.6 Iterative Methods tbr Linear Systems 156
3.7 Iteration for Non]inear Systems: Seide1 and
Newton's Methods (Optiona1) i67
4 Interpolation and Polynomial
Approximation 186
4.1 Taylor Series and Calculation of Functions I87
4.2 Introduction to Interpolation i99
4.3 Lagrange Approximation 206
4.4 Newton Po1ynomials 220
4.5 Chebyshev Polynomials (Optional) 230
4.6 Pade Approximations 243
5 Curve Fitting 252
5.1 Least-squares Line 253
5.2 Curve Fitting 263
5.3 Interpolation by Spline Functions 279
5.4 Fourier Series and Trigonometric Polynomia1s 297
6 Numerical Differentiation 310
6.1 Approximating The Derivative 311
6.2 Numerical Differentiation Formulas 329
7 Numerical Integration J42
7.1 Introduction to Quadrature 343
7.2 Composite Trapezoidal and Simpson's Rule 354
7.3 Recursive Rules and Romberg Integration 368
7.4 Adaptive Quadrature 382
7.5 Gauss-Legendre Integration (Optional) 389
8 Numerical Optimization 399
8.1 Minimization of a Function 400
9 Solution of Differential Equations 426
9.1 Introduction to Differential Equations 427
9.2 Euler's Method Jj3
9.3 Heun's Method 443
9.4 Taylor Series Method 451
9.5 Runge-Kutta Methods 458
9.6 Predictor-Corrector Methods 474
9.7 Systems of Differential Equations 487
9.8 Boundary Value Problems 497
9.9 Finite-difference Method 505
10 Solution of Partial Differential Equations S14
10.1 Hyperbolic Equations 516
10.2 Parabolic Equations 526
10.3 Elliptic Equations 538
11 Eigenvalues and Eigenvectors 555
11.1 Homogeneous Systems f The Eigenvalue Problem 556
11.2 Power Method 568
11.3 Jacobi's Method 581
11.4 Eigenvalues of Symmetric Matrices 594
Appendix: An Introduction to MATLAB 608
Some Suggested References for Reports 616
Bibliography and References 619
Answers to Selected Exercises 631
Index 655
