An introduction to numerical analysis for electrical and computer engineers / Christopher J. Zarowski.

Format:

Book

Author/Creator:

Zarowski, Christopher J.

Language:

English

Subjects (All):

Electrical engineering--Mathematics.

Electrical engineering.

Computer science--Mathematics.

Computer science.

Numerical analysis.

Physical Description:

1 online resource (604 p.)

Edition:

1st ed.

Place of Publication:

Hoboken, NJ : Wiley, c2004.

Language Note:

English

Summary:

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

Contents:

AN INTRODUCTION TO NUMERICAL ANALYSIS FOR ELECTRICAL AND COMPUTER ENGINEERS; CONTENTS; Preface; 1 Functional Analysis Ideas; 1.1 Introduction; 1.2 Some Sets; 1.3 Some Special Mappings: Metrics, Norms, and Inner Products; 1.3.1 Metrics and Metric Spaces; 1.3.2 Norms and Normed Spaces; 1.3.3 Inner Products and Inner Product Spaces; 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; 7.4.1 The Method; 7.4.2 Rate of Convergence Analysis

7.4.3 Breakdown Phenomena 7.5 Systems of Nonlinear Equations; 7.5.1 Fixed-Point Method; 7.5.2 Newton-Raphson Method; 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

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

ISBN:

9786610368174

9781280368172

1280368179

9780470357651

0470357657

9780471650409

0471650404

9780471650416

0471650412

OCLC:

70720124