Christopher J. Zarowski

An Introduction to Numerical Analysis for Electrical and Computer Engineers (eBook, PDF)

• Format: PDF

Produktbeschreibung

* 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 An Instructor's Manual presenting detailed solutions to all the problems in the book is available from the Wiley editorial department.

Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 604
• Erscheinungstermin: 29. April 2004
• Englisch
• ISBN-13: 9780471650409
• Artikelnr.: 37302145

Autorenporträt

Christopher?J. Zarowski, PhD,?is an associate professor?in the? Department of Electrical and Computer Engineering at the ?University of Alberta, Canada. His research areas include digital communications applications (wireless, wireline, optical fiber), biomedical applications (e.g., circadian rhythm parameter estimation), structured matrix algebra, wavelet methods, signal detection and parameter estimation, computationally efficient and numerically reliable algorithms, and parallel processing algorithms. He has authored over 100 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.

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)