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E-raamat: Applied Numerical Methods Using MATLAB

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(Chung-Ang University, Korea), (Materials Research Lab, Pennsylvania State University), (University of Auckland, New Zealand), (Chung-Ang University, Korea)
  • Formaat: PDF+DRM
  • Ilmumisaeg: 20-May-2005
  • Kirjastus: Wiley-Interscience
  • Keel: eng
  • ISBN-13: 9780471705185
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Applied Numerical Methods Using MATLABSuurem pilt
  • Formaat: PDF+DRM
  • Ilmumisaeg: 20-May-2005
  • Kirjastus: Wiley-Interscience
  • Keel: eng
  • ISBN-13: 9780471705185
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MATLAB is a high-level software package used by many engineers and scientists. Yang (electrical engineering Chung-Ang U., Korea), along with colleagues in the US and New Zealand, introduces applied numerical methods for nonmath majors with little programing background or desire to derive the underlying mathematics. Algorithms and examples of applications of similar functions are followed by MATLAB code to adapt to solving sample problems. A comparison of different methods is also included. Indexing is by subject, MATLAB routine, and table. Mathematical material is appended. Annotation ©2005 Book News, Inc., Portland, OR (booknews.com)

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.

Arvustused

"For academic libraries, mathematicians, students, and working professionalshighly recommended." (CHOICE, November 2005)

Preface xiii
MATLAB Usage and Computational Errors
1(70)
Basic Operations of MATLAB
1(26)
Input/Output of Data from MATLAB Command Window
2(1)
Input/Output of Data Through Files
2(2)
Input/Output of Data Using Keyboard
4(1)
2-D Graphic Input/Output
5(5)
3-D Graphic Output
10(1)
Mathematical Functions
10(5)
Operations on Vectors and Matrices
15(7)
Random Number Generators
22(2)
Flow Control
24(3)
Computer Errors Versus Human Mistakes
27(10)
IEEE 64-bit Floating-Point Number Representation
28(3)
Various Kinds of Computing Errors
31(2)
Absolute/Relative Computing Errors
33(1)
Error Propagation
33(1)
Tips for Avoiding Large Errors
34(3)
Toward Good Program
37(34)
Nested Computing for Computational Efficiency
37(2)
Vector Operation Versus Loop Iteration
39(1)
Iterative Routine Versus Nested Routine
40(1)
To Avoid Runtime Error
40(4)
Parameter Sharing via Global Variables
44(1)
Parameter Passing Through Varargin
45(1)
Adaptive Input Argument List
46(1)
Problems
46(25)
System of Linear Equations
71(46)
Solution for a System of Linear Equations
72(7)
The Nonsingular Case (M = N)
72(1)
The Underdetermined Case (M < N): Minimum-Norm Solution
72(3)
The Overdetermined Case (M > N): Least-Squares Error Solution
75(1)
RLSE (Recursive Least-Squares Estimation)
76(3)
Solving a System of Linear Equations
79(13)
Gauss Elimination
79(2)
Partial Pivoting
81(8)
Gauss--Jordan Elimination
89(3)
Inverse Matrix
92(1)
Decomposition (Factorization)
92(6)
LU Decomposition (Factorization): Triangularization
92(5)
Other Decomposition (Factorization): Cholesky, QR, and SVD
97(1)
Iterative Methods to Solve Equations
98(19)
Jacobi Iteration
98(2)
Gauss--Seidel Iteration
100(3)
The Convergence of Jacobi and Gauss--Seidel Iterations
103(1)
Problems
104(13)
Interpolation and Curve Fitting
117(62)
Interpolation by Lagrange Polynomial
117(2)
Interpolation by Newton Polynomial
119(5)
Approximation by Chebyshev Polynomial
124(5)
Pade Approximation by Rational Function
129(4)
Interpolation by Cubic Spline
133(6)
Hermite Interpolating Polynomial
139(2)
Two-dimensional Interpolation
141(2)
Curve Fitting
143(7)
Straight Line Fit: A Polynomial Function of First Degree
144(1)
Polynomial Curve Fit: A Polynomial Function of Higher Degree
145(4)
Exponential Curve Fit and Other Functions
149(1)
Fourier Transform
150(29)
FFT Versus DFT
151(1)
Physical Meaning of DFT
152(3)
Interpolation by Using DFS
155(2)
Problems
157(22)
Nonlinear Equations
179(30)
Iterative Method Toward Fixed Point
179(4)
Bisection Method
183(2)
False Position or Regula Falsi Method
185(1)
Newton(--Raphson) Method
186(3)
Secant Method
189(2)
Newton Method for a System of Nonlinear Equations
191(2)
Symbolic Solution for Equations
193(1)
A Real-World Problem
194(15)
Problems
197(12)
Numerical Differentiation/Integration
209(54)
Difference Approximation for First Derivative
209(2)
Approximation Error of First Derivative
211(5)
Difference Approximation for Second and Higher Derivative
216(4)
Interpolating Polynomial and Numerical Differential
220(2)
Numerical Integration and Quadrature
222(4)
Trapezoidal Method and Simpson Method
226(2)
Recursive Rule and Romberg Integration
228(3)
Adaptive Quadrature
231(3)
Gauss Quadrature
234(7)
Gauss--Legendre Integration
235(3)
Gauss--Hermite Integration
238(1)
Gauss--Laguerre Integration
239(1)
Gauss--Chebyshev Integration
240(1)
Double Integral
241(22)
Problems
244(19)
Ordinary Differential Equations
263(58)
Euler's Method
263(3)
Heun's Method: Trapezoidal Method
266(1)
Runge--Kutta Method
267(2)
Predictor--Corrector Method
269(8)
Adams--Bashforth--Moulton Method
269(4)
Hamming Method
273(1)
Comparison of Methods
274(3)
Vector Differential Equations
277(10)
State Equation
277(4)
Discretization of LTI State Equation
281(2)
High-Order Differential Equation to State Equation
283(1)
Stiff Equation
284(3)
Boundary Value Problem (BVP)
287(34)
Shooting Method
287(3)
Finite Difference Method
290(3)
Problems
293(28)
Optimization
321(50)
Unconstrained Optimization [ L-2,
Chapter 7]
321(22)
Golden Search Method
321(2)
Quadratic Approximation Method
323(2)
Nelder--Mead Method [ W-8]
325(3)
Steepest Descent Method
328(2)
Newton Method
330(2)
Conjugate Gradient Method
332(2)
Simulated Annealing Method [ W-7]
334(4)
Genetic Algorithm [ W-7]
338(5)
Constrained Optimization [ L-2,
Chapter 10]
343(7)
Lagrange Multiplier Method
343(3)
Penalty Function Method
346(4)
MATLAB Built-In Routines for Optimization
350(21)
Unconstrained Optimization
350(2)
Constrained Optimization
352(3)
Linear Programming (LP)
355(2)
Problems
357(14)
Matrices and Eigenvalues
371(30)
Eigenvalues and Eigenvectors
371(2)
Similarity Transformation and Diagonalization
373(5)
Power Method
378(3)
Scaled Power Method
378(2)
Inverse Power Method
380(1)
Shifted Inverse Power Method
380(1)
Jacobi Method
381(4)
Physical Meaning of Eigenvalues/Eigenvectors
385(4)
Eigenvalue Equations
389(12)
Problems
390(11)
Partial Differential Equations
401(60)
Elliptic PDE
402(4)
Parabolic PDE
406(8)
The Explicit Forward Euler Method
406(1)
The Implicit Backward Euler Method
407(2)
The Crank--Nicholson Method
409(3)
Two-Dimensional Parabolic PDE
412(2)
Hyperbolic PDE
414(6)
The Explicit Central Difference Method
415(2)
Two-Dimensional Hyperbolic PDE
417(3)
Finite Element Method (FEM) for solving PDE
420(9)
GUI of MATLAB for Solving PDEs: PDETOOL
429(32)
Basic PDEs Solvable by PDETOOL
430(1)
The Usage of PDETOOL
431(4)
Examples of Using PDETOOL to Solve PDEs
435(9)
Problems
444(17)
Appendix A. Mean Value Theorem 461(2)
Appendix B. Matrix Operations/Properties 463(8)
Appendix C. Differentiation with Respect to a Vector 471(2)
Appendix D. Laplace Transform 473(2)
Appendix E. Fourier Transform 475(2)
Appendix F. Useful Formulas 477(4)
Appendix G. Symbolic Computation 481(8)
Appendix H. Sparse Matrices 489(2)
Appendix I. MATLAB 491(6)
References 497(2)
Subject Index 499(4)
Index for MATLAB Routines 503(6)
Index for Tables 509


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.
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