|  | Yang, Won Young / Cao, Wenwu / Chung, Tae-Sang / Morris, John
Applied Numerical Methods Using MATLAB
 1. Auflage Juni 2005
119,- Euro
2005. 528 Seiten, Hardcover
ISBN 978-0-471-69833-3 - John Wiley & Sons
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| Kurzbeschreibung
In recent years, with the introduction of new media products, there has been a shift in the use of programming languages from FORTRAN or C to MATLAB for implementing numerical methods. This book makes use of the powerful MATLAB software to avoid complex derivations, and to teach the fundamental concepts using the software to solve practical problems. Over the years, many textbooks have been written on the subject of numerical methods. Based on their course experience, the authors use a more practical approach and link every method to real engineering and/or science problems. The main idea is that engineers don't have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems.
Aus dem Inhalt
Preface.
1 MATLAB Usage and Computational Errors.
1.1 Basic Operations of MATLAB.
1.2 Computer Errors Versus Human Mistakes.
1.3 Toward Good Program.
Problems.
2 System of Linear Equations.
2.1 Solution for a System of Linear Equations.
2.2 Solving a System of Linear Equations.
2.3 Inverse Matrix.
2.4 Decomposition (Factorization).
2.5 Iterative Methods to Solve Equations.
Problems.
3 Interpolation and Curve Fitting.
3.1 Interpolation by Lagrange Polynomial.
3.2 Interpolation by Newton Polynomial.
3.3 Approximation by Chebyshev Polynomial.
3.4 Pade Approximation by Rational Function.
3.5 Interpolation by Cubic Spline.
3.6 Hermite Interpolating Polynomial.
3.7 Two-dimensional Interpolation.
3.8 Curve Fitting.
3.9 Fourier Transform.
Problems.
4 Nonlinear Equations.
4.1 Iterative Method Toward Fixed Point.
4.2 Bisection Method.
4.3 False Position or Regula Falsi Method.
4.4 Newton(-Raphson) Method.
4.5 Secant Method.
4.6 Newton Method for a System of Nonlinear Equations.
4.7 Symbolic Solution for Equations.
4.8 A Real-World Problem.
Problems.
5 Numerical Differentiation/Integration.
5.1 Difference Approximation for First Derivative.
5.2 Approximation Error of First Derivative.
5.3 Difference Approximation for Second and Higher Derivative.
5.4 Interpolating Polynomial and Numerical Differential.
5.5 Numerical Integration and Quadrature.
5.6 Trapezoidal Method and Simpson Method.
5.7 Recursive Rule and Romberg Integration.
5.8 Adaptive Quadrature.
5.9 Gauss Quadrature.
5.10 Double Integral.
Problems.
6 Ordinary Differential Equations.
6.1 Euler's Method.
6.2 Heun's Method: Trapezoidal Method.
6.3 Runge-Kutta Method.
6.4 Predictor-Corrector Method.
6.5 Vector Differential Equations.
6.6 Boundary Value Problem (BVP).
Problems.
7 Optimization.
7.1 Unconstrained Optimization [L-2, Chapter 7].
7.2 Constrained Optimization [L-2, Chapter 10].
7.3 MATLAB Built-In Routines for Optimization.
Problems.
8 Matrices and Eigenvalues.
8.1 Eigenvalues and Eigenvectors.
8.2 Similarity Transformation and Diagonalization.
8.3 Power Method.
8.4 Jacobi Method.
8.5 Physical Meaning of Eigenvalues/Eigenvectors.
8.6 Eigenvalue Equations.
Problems.
9 Partial Differential Equations.
9.1 Elliptic PDE.
9.2 Parabolic PDE.
9.3 Hyperbolic PDE.
9.4 Finite Element Method (FEM) for solving PDE.
9.5 GUI of MATLAB for Solving PDEs: PDETOOL.
Problems.
Appendix A. Mean Value Theorem.
Appendix B. Matrix Operations/Properties.
Appendix C. Differentiation with Respect to a Vector.
Appendix D. Laplace Transform.
Appendix E. Fourier Transform.
Appendix F. Useful Formulas.
Appendix G. Symbolic Computation.
Appendix H. Sparse Matrices.
Appendix I. MATLAB.
References.
Subject Index.
Index for MATLAB Routines.
Index for Tables.
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