Numerical Methods (4TH)

個数:

Numerical Methods (4TH)

  • 在庫がございません。海外の書籍取次会社を通じて出版社等からお取り寄せいたします。
    通常6~9週間ほどで発送の見込みですが、商品によってはさらに時間がかかることもございます。
    重要ご説明事項
    1. 納期遅延や、ご入手不能となる場合がございます。
    2. 複数冊ご注文の場合、分割発送となる場合がございます。
    3. 美品のご指定は承りかねます。
  • ≪洋書のご注文につきまして≫ 「海外取次在庫あり」および「国内仕入れ先からお取り寄せいたします」表示の商品でも、納期の目安期間内にお届けできないことがございます。あらかじめご了承ください。

  • 製本 Hardcover:ハードカバー版/ページ数 591 p.
  • 言語 ENG,ENG
  • 商品コード 9780495114765
  • DDC分類 515

Full Description


NUMERICAL METHODS, Fourth Edition emphasizes the intelligent application of approximation techniques to the type of problems that commonly occur in engineering and the physical sciences. Readers learn why the numerical methods work, what kinds of errors to expect, and when an application might lead to difficulties. The authors also provide information about the availability of high-quality software for numerical approximation routines. The techniques are the same as those covered in the authors' top-selling Numerical Analysis text, but this text provides an overview for students who need to know the methods without having to perform the analysis. This concise approach still includes mathematical justifications, but only when they are necessary to understand the methods. The emphasis is placed on describing each technique from an implementation standpoint, and on convincing the reader that the method is reasonable both mathematically and computationally.

Table of Contents

Preface                                            ix
1 Mathematical Preliminaries and Error 1 (32)
Analysis
1.1 Introduction 1 (1)
1.2 Review of Calculus 1 (14)
1.3 Round-Off Error and Computer 15 (7)
Arithmetic
1.4 Errors in Scientific Computation 22 (7)
1.5 Computer Software 29 (4)
2 Solutions of Equations of One Variable 33 (30)
2.1 Introduction 33 (1)
2.2 The Bisection Method 33 (5)
2.3 The Secant Method 38 (6)
2.4 Newton's Method 44 (7)
2.5 Error Analysis and Accelerating 51 (3)
Convergence
2.6 Muller's Method 54 (6)
2.7 Survey of Methods and Software 60 (3)
3 Interpolation and Polynomial Approximation 63 (44)
3.1 Introduction 63 (2)
3.2 Lagrange Polynomials 65 (10)
3.3 Divided Differences 75 (8)
3.4 Hermite Interpolation 83 (4)
3.5 Spline Interpolation 87 (12)
3.6 Parametric Curves 99 (6)
3.7 Survey of Methods and Software 105(2)
4 Numerical Integration and Differentiation 107(66)
4.1 Introduction 107(1)
4.2 Basic Quadrature Rules 107(8)
4.3 Composite Quadrature Rules 115(9)
4.4 Romberg Integration 124(8)
4.5 Gaussian Quadrature 132(6)
4.6 Adaptive Quadrature 138(7)
4.7 Multiple Integrals 145(12)
4.8 Improper Integrals 157(6)
4.9 Numerical Differentiation 163(9)
4.10 Survey of Methods and Software 172(1)
5 Numerical Solution of Initial-Value 173(56)
Problems
5.1 Introduction 173(1)
5.2 Taylor Methods 174(9)
5.3 Runge-Kutta Methods 183(8)
5.4 Predictor-Corrector Methods 191(7)
5.5 Extrapolation Methods 198(6)
5.6 Adaptive Techniques 204(10)
5.7 Methods for Systems of Equations 214(8)
5.8 Stiff Differential Equations 222(5)
5.9 Survey of Methods and Software 227(2)
6 Direct Methods for Solving Linear Systems 229(48)
6.1 Introduction 229(1)
6.2 Gaussian Elimination 229(11)
6.3 Pivoting Strategies 240(7)
6.4 Linear Algebra and Matrix Inversion 247(13)
6.5 Matrix Factorization 260(6)
6.6 Techniques for Special Matrices 266(9)
6.7 Survey of Methods and Software 275(2)
7 Iterative Methods for Solving Linear 277(44)
Systems
7.1 Introduction 277(1)
7.2 Convergence of Vectors 277(8)
7.3 Eigenvalues and Eigenvectors 285(7)
7.4 The Jacobi and Gauss-Seidel Methods 292(6)
7.5 The SOR Method 298(4)
7.6 Error Bounds and Iterative Refinement 302(7)
7.7 The Conjugate Gradient Method 309(9)
7.8 Survey of Methods and Software 318(3)
8 Approximation Theory 321(42)
8.1 Introduction 321(1)
8.2 Discrete Least Squares Approximation 321(8)
8.3 Continuous Least Squares Approximation 329(9)
8.4 Chebyshev Polynomials 338(6)
8.5 Rational Function Approximation 344(5)
8.6 Trigonometric Polynomial Approximation 349(6)
8.7 Fast Fourier Transforms 355(6)
8.8 Survey of Methods and Software 361(2)
9 Approximating Eigenvalues 363(50)
9.1 Introduction 363(1)
9.2 Linear Algebra and Eigenvalues 363(10)
9.3 The Power Method 373(12)
9.4 Householder's Method 385(5)
9.5 The QR Method 390(9)
9.6 Singular Value Decomposition 399(11)
9.7 Survey of Methods and Software 410(3)
10 Systems of Nonlinear Equations 413(28)
10.1 Introduction 413(3)
10.2 Newton's Method for Systems 416(5)
10.3 Quasi-Newton Methods 421(6)
10.4 The Steepest Descent Method 427(5)
10.5 Homotopy and Continuation Methods 432(7)
10.6 Survey of Methods and Software 439(2)
11 Boundary-Value Problems for Ordinary 441(34)
Differential Equations
11.1 Introduction 441(1)
11.2 The Linear Shooting Method 441(5)
11.3 Linear Finite Difference Methods 446(6)
11.4 The Nonlinear Shooting Method 452(6)
11.5 Nonlinear Finite-Difference Methods 458(3)
11.6 Variational Techniques 461(12)
11.7 Survey of Methods and Software 473(2)
12 Numerical Methods for 475(44)
Partial-Differential Equations
12.1 Introduction 475(1)
12.2 Finite-Difference Methods for 475(8)
Elliptic Problems
12.3 Finite-Difference Methods for 483(14)
Parabolic Problems
12.4 Finite-Difference Methods for 497(6)
Hyperbolic Problems
12.5 Introduction to the Finite-Element 503(14)
Method
12.6 Survey of Methods and Software 517(2)
Bibliography 519(6)
Answers to Odd Exercises 525(60)
Index 585