_ This book is an introduction to numerical analysis and intends to strike a balance between analytical rigor and the treatment of particular methods for engineering problems _ Emphasizes the earlier stages of numerical analysis for engineers with real-life problem-solving solutions applied to computing and engineering _ Includes MATLAB oriented examples
_ This book is an introduction to numerical analysis and intends to strike a balance between analytical rigor and the treatment of particular methods for engineering problems _ Emphasizes the earlier stages of numerical analysis for engineers with real-life problem-solving solutions applied to computing and engineering _ Includes MATLAB oriented examples
CHRISTOPHER J. ZAROWSKI, PhD, is an associate professor in the Department of Electrical and Computer Engineering at the University of Alberta, Canada. He has authored more than fifty journal articles and conference papers and is a senior member of the IEEE.
Inhaltsangabe
Preface. 1 Functional Analysis Ideas. 1.1 Introduction. 1.2 Some Sets. 1.3 Some Special Mappings: Metrics, Norms, and Inner Products. 1.4 The Discrete Fourier Series (DFS). Appendix 1.A Complex Arithmetic. Appendix 1.B Elementary Logic. References. Problems. 2 Number Representations. 2.1 Introduction. 2.2 Fixed-Point Representations. 2.3 Floating-Point Representations. 2.4 Rounding Effects in Dot Product Computation. 2.5 Machine Epsilon. Appendix 2.A Review of Binary Number Codes. References. Problems. 3 Sequences and Series. 3.1 Introduction. 3.2 Cauchy Sequences and Complete Spaces. 3.3 Pointwise Convergence and Uniform Convergence. 3.4 Fourier Series. 3.5 Taylor Series. 3.6 Asymptotic Series. 3.7 More on the Dirichlet Kernel. 3.8 Final Remarks. Appendix 3.A COordinate Rotation DIgital Computing (CORDIC). 3.A.1 Introduction. 3.A.2 The Concept of a Discrete Basis. 3.A.3 Rotating Vectors in the Plane. 3.A.4 Computing Arctangents. 3.A.5 Final Remarks. Appendix 3.B Mathematical Induction. Appendix 3.C Catastrophic Cancellation. References. Problems. 4 Linear Systems of Equations. 4.1 Introduction. 4.2 Least-Squares Approximation and Linear Systems. 4.3 Least-Squares Approximation and Ill-Conditioned Linear Systems. 4.4 Condition Numbers. 4.5 LU Decomposition. 4.6 Least-Squares Problems and QR Decomposition. 4.7 Iterative Methods for Linear Systems. 4.8 Final Remarks. Appendix 4.A Hilbert Matrix Inverses. Appendix 4.B SVD and Least Squares. References. Problems. 5 Orthogonal Polynomials. 5.1 Introduction. 5.2 General Properties of Orthogonal Polynomials. 5.3 Chebyshev Polynomials. 5.4 Hermite Polynomials. 5.5 Legendre Polynomials. 5.6 An Example of Orthogonal Polynomial Least-Squares Approximation. 5.7 Uniform Approximation. References. Problems. 6 Interpolation. 6.1 Introduction. 6.2 Lagrange Interpolation. 6.3 Newton Interpolation. 6.4 Hermite Interpolation. 6.5 Spline Interpolation. References. Problems. 7 Nonlinear Systems of Equations. 7.1 Introduction. 7.2 Bisection Method. 7.3 Fixed-Point Method. 7.4 Newton-Raphson Method. 7.5 Systems of Nonlinear Equations. 7.6 Chaotic Phenomena and a Cryptography Application. References. Problems. 8 Unconstrained Optimization. 8.1 Introduction. 8.2 Problem Statement and Preliminaries. 8.3 Line Searches. 8.4 Newton's Method. 8.5 Equality Constraints and Lagrange Multipliers. Appendix 8.A MATLAB Code for Golden Section Search. References. Problems. 9 Numerical Integration and Differentiation. 9.1 Introduction. 9.2 Trapezoidal Rule. 9.3 Simpson's Rule. 9.4 Gaussian Quadrature. 9.5 Romberg Integration. 9.6 Numerical Differentiation. References. Problems. 10 Numerical Solution of Ordinary Differential Equations. 10.1 Introduction. 10.2 First-Order ODEs. 10.3 Systems of First-Order ODEs. 10.4 Multistep Methods for ODEs. 10.5 Variable-Step-Size (Adaptive) Methods for ODEs. 10.6 Stiff Systems. 10.7 Final Remarks. Appendix 10.A MATLAB Code for Example 10.8. Appendix 10.B MATLAB Code for Example 10.13. References. Problems. 11 Numerical Methods for Eigenproblems. 11.1 Introduction. 11.2 Review of Eigenvalues and Eigenvectors. 11.3 The Matrix Exponential. 11.4 The Power Methods. 11.5 QR Iterations. References. Problems. 12 Numerical Solution of Partial Differential Equations. 12.1 Introduction. 12.2 A Brief Overview of Partial Differential Equations. 12.3 Applications of Hyperbolic PDEs. 12.4 The Finite-Difference (FD) Method. 12.5 The Finite-Difference Time-Domain (FDTD) Method. Appendix 12.A MATLAB Code for Example 12.5. References. Problems. 13 An Introduction to MATLAB. 13.1 Introduction. 13.2 Startup. 13.3 Some Basic Operators, Operations, and Functions. 13.4 Working with Polynomials. 13.5 Loops. 13.6 Plotting and M-Files. References. Index.
Preface. 1 Functional Analysis Ideas. 1.1 Introduction. 1.2 Some Sets. 1.3 Some Special Mappings: Metrics, Norms, and Inner Products. 1.4 The Discrete Fourier Series (DFS). Appendix 1.A Complex Arithmetic. Appendix 1.B Elementary Logic. References. Problems. 2 Number Representations. 2.1 Introduction. 2.2 Fixed-Point Representations. 2.3 Floating-Point Representations. 2.4 Rounding Effects in Dot Product Computation. 2.5 Machine Epsilon. Appendix 2.A Review of Binary Number Codes. References. Problems. 3 Sequences and Series. 3.1 Introduction. 3.2 Cauchy Sequences and Complete Spaces. 3.3 Pointwise Convergence and Uniform Convergence. 3.4 Fourier Series. 3.5 Taylor Series. 3.6 Asymptotic Series. 3.7 More on the Dirichlet Kernel. 3.8 Final Remarks. Appendix 3.A COordinate Rotation DIgital Computing (CORDIC). 3.A.1 Introduction. 3.A.2 The Concept of a Discrete Basis. 3.A.3 Rotating Vectors in the Plane. 3.A.4 Computing Arctangents. 3.A.5 Final Remarks. Appendix 3.B Mathematical Induction. Appendix 3.C Catastrophic Cancellation. References. Problems. 4 Linear Systems of Equations. 4.1 Introduction. 4.2 Least-Squares Approximation and Linear Systems. 4.3 Least-Squares Approximation and Ill-Conditioned Linear Systems. 4.4 Condition Numbers. 4.5 LU Decomposition. 4.6 Least-Squares Problems and QR Decomposition. 4.7 Iterative Methods for Linear Systems. 4.8 Final Remarks. Appendix 4.A Hilbert Matrix Inverses. Appendix 4.B SVD and Least Squares. References. Problems. 5 Orthogonal Polynomials. 5.1 Introduction. 5.2 General Properties of Orthogonal Polynomials. 5.3 Chebyshev Polynomials. 5.4 Hermite Polynomials. 5.5 Legendre Polynomials. 5.6 An Example of Orthogonal Polynomial Least-Squares Approximation. 5.7 Uniform Approximation. References. Problems. 6 Interpolation. 6.1 Introduction. 6.2 Lagrange Interpolation. 6.3 Newton Interpolation. 6.4 Hermite Interpolation. 6.5 Spline Interpolation. References. Problems. 7 Nonlinear Systems of Equations. 7.1 Introduction. 7.2 Bisection Method. 7.3 Fixed-Point Method. 7.4 Newton-Raphson Method. 7.5 Systems of Nonlinear Equations. 7.6 Chaotic Phenomena and a Cryptography Application. References. Problems. 8 Unconstrained Optimization. 8.1 Introduction. 8.2 Problem Statement and Preliminaries. 8.3 Line Searches. 8.4 Newton's Method. 8.5 Equality Constraints and Lagrange Multipliers. Appendix 8.A MATLAB Code for Golden Section Search. References. Problems. 9 Numerical Integration and Differentiation. 9.1 Introduction. 9.2 Trapezoidal Rule. 9.3 Simpson's Rule. 9.4 Gaussian Quadrature. 9.5 Romberg Integration. 9.6 Numerical Differentiation. References. Problems. 10 Numerical Solution of Ordinary Differential Equations. 10.1 Introduction. 10.2 First-Order ODEs. 10.3 Systems of First-Order ODEs. 10.4 Multistep Methods for ODEs. 10.5 Variable-Step-Size (Adaptive) Methods for ODEs. 10.6 Stiff Systems. 10.7 Final Remarks. Appendix 10.A MATLAB Code for Example 10.8. Appendix 10.B MATLAB Code for Example 10.13. References. Problems. 11 Numerical Methods for Eigenproblems. 11.1 Introduction. 11.2 Review of Eigenvalues and Eigenvectors. 11.3 The Matrix Exponential. 11.4 The Power Methods. 11.5 QR Iterations. References. Problems. 12 Numerical Solution of Partial Differential Equations. 12.1 Introduction. 12.2 A Brief Overview of Partial Differential Equations. 12.3 Applications of Hyperbolic PDEs. 12.4 The Finite-Difference (FD) Method. 12.5 The Finite-Difference Time-Domain (FDTD) Method. Appendix 12.A MATLAB Code for Example 12.5. References. Problems. 13 An Introduction to MATLAB. 13.1 Introduction. 13.2 Startup. 13.3 Some Basic Operators, Operations, and Functions. 13.4 Working with Polynomials. 13.5 Loops. 13.6 Plotting and M-Files. References. Index.
Rezensionen
"Zarkowski (Univ. of Alberta) offers this book as a general, advanced undergraduate work in numerical analysis, containing all of the usual topics." ( CHOICE , October 2004)
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