Applied Numerical Methods using MATLAB
(Sprache: Englisch)
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...
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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.
Klappentext zu „Applied Numerical Methods using MATLAB “
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 benefit is that engineers don t have to know the mathematical theory in order to apply the numerical methods for solving their real-life problems.An Instructor s Manual presenting detailed solutions to all the problems in the book is available online.
Learn how to use MATLAB(r) to solve complex numerical problems
Increasingly, scientists and engineers favor MATLAB over conventional programming languages such as FORTRAN and C when they wish to solve complex problems. This book will enable readers to solve problems without needing to understand all the details of the underlying theory of numerical methods. By providing many examples of the uses of similar functions, it guides them towards the selection of the appropriate MATLAB functions for solving their problem efficiently.
The authors have incorporated existing MATLAB functions into a series of simplified, yet complete programs that may be readily adapted by students and practitioners to solve real-world engineering and science problems. Key features include:
* More than 100 supplemental codes
* Complete MATLAB programs to demonstrate solutions to real-life
* exercises and problems
* Downloadable MATLAB programs to correspond with the text
* Interactive demonstration programs that course instructors can use to produce visual presentations of the solution processes of some algorithms
* An overview of the Partial Differential Equation (PDE) toolbox
* An appendix with MATLAB commands/functions for symbolic computation
With very little prior programming experience, students and practitioners will find this approach invaluable to quickly learn how to solve their numerical problems.
Increasingly, scientists and engineers favor MATLAB over conventional programming languages such as FORTRAN and C when they wish to solve complex problems. This book will enable readers to solve problems without needing to understand all the details of the underlying theory of numerical methods. By providing many examples of the uses of similar functions, it guides them towards the selection of the appropriate MATLAB functions for solving their problem efficiently.
The authors have incorporated existing MATLAB functions into a series of simplified, yet complete programs that may be readily adapted by students and practitioners to solve real-world engineering and science problems. Key features include:
* More than 100 supplemental codes
* Complete MATLAB programs to demonstrate solutions to real-life
* exercises and problems
* Downloadable MATLAB programs to correspond with the text
* Interactive demonstration programs that course instructors can use to produce visual presentations of the solution processes of some algorithms
* An overview of the Partial Differential Equation (PDE) toolbox
* An appendix with MATLAB commands/functions for symbolic computation
With very little prior programming experience, students and practitioners will find this approach invaluable to quickly learn how to solve their numerical problems.
Inhaltsverzeichnis zu „Applied Numerical Methods using MATLAB “
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
... mehr
Optimization [L-2, Chapter 10].
7.3 MATLAB Built-In Routines for Optimization.
Problems.
8 Matricesand 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.
7.3 MATLAB Built-In Routines for Optimization.
Problems.
8 Matricesand 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.
... weniger
Autoren-Porträt
WON Y. YANG, PhD, is Professor of Electrical Engineering at Chung-Ang University, Korea. WENWU CAO, PhD, is Professor of Mathematics and Materials Science at The Pennsylvania State University. TAE-SANG CHUNG, PhD, is Professor of Electrical Engineering at Chung-Ang University, Korea. JOHN MORRIS, PhD, is Associate Professor of Computer Science and Electrical and Computer Engineering at The University of Auckland, New Zealand.
Bibliographische Angaben
- 2005, 1. Auflage., 528 Seiten, Maße: 23,9 cm, Gebunden, Englisch
- By Won Young Yang, Wenwu Cao, Tae-Sang Chung et al.
- Verlag: Wiley & Sons
- ISBN-10: 0471698334
- ISBN-13: 9780471698333
Sprache:
Englisch
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