Advanced Engineering Mathematics with MATLAB / Edition 2

by Thomas L. Harman, James B. Dabney, Norman John Richert

Overview

ADVANCED ENGINEERING MATHEMATICS WITH MATLAB is written for engineers and engineering students who are interested in applying MATLAB to solve practical engineering problems. The book emphasizes mathematical principles, not computations, with MATLAB employed as a tool for analysis that shows how engineering problems are defined and solved. The book features complete MATLAB integration throughout, abundant examples which show real practical applications, and end-of-chapter problems that reinforce techniques.

Product Details

ISBN-13:	9780534371647
Publisher:	CL Engineering
Publication date:	12/29/1999
Series:	Electrical Engineering Series
Edition description:	REV
Pages:	788
Product dimensions:	7.67(w) x 9.56(h) x 1.39(d)

About the Author

Dr. Thomas Harman is Professor and Chair of the Engineering Division at Rice University. He earned his B.S.E.E. with Honors from the University of Maryland in 1965 and his Ph.D. from Rice University in Electrical Engineering in 1972.

Dr. James B. Dabney is Assistant Professor of Systems Engineering at University of Houston - Clear Lake. He earned his B.S. in 1974 from Virginia Polytechnic Institute and State University, his M.S. in 1993 University of Houston - Clear Lake and his Ph.D. in 1998 Rice University.

Norman John Richert of the University of Houston-Clear Lake.

Table of Contents

1. INTRODUCTION Introduction to MATLAB / MATLAB Commands for Display and Plotting / Creating MATLAB Programs / MATLAB Programming Language / Problem Solving and Programming (Optional) / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 2. NUMBERS AND VECTORS Properties of Real Numbers / MATLAB Computer Numbers (Optional) / Complex Numbers / Vectors in Two Dimensions and Three Dimensions / Vectors in Higher Dimensions / MATLAB Vectors / Complex Vectors / Vector Spaces / Vector Spaces of Functions / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 3. MATRICES Basic Properties of Matrices / MATLAB Matrix Operations / Square and Symmetric Matrices / Determinants and Matrix Inverses / Orthogonal and Triangular Matrices / Systems of Linear Equations / MATLAB Matrix Functions / Linear Transformations / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 4. EIGENVALUES AND EIGENVECTORS General Discussion of Eigenvalues / Eigenvalues and Eigenvectors / Matrix Eigenvalue Theorems / Complex Vectors and Matrices / MATLAB Commands for Eigenvectors / Matrix Calculus / Similar and Diagonalizable Matrices / Special Matrices and Their Eigenvalues (Optional) / Applications to Differential Equations / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 5. LINEAR DIFFERENTIAL EQUATIONS Classification of Differential Equations / Linear Differential Equations / Higher Order Differential Equations / Second Order Differential Equations / Particular Solutions of Differential Equations / Systems of Differential Equations / MATLAB Solutions of Systems of Differential Equations / Homogeneous Systems with Repeated Eigenvalues / Nonhomogeneous Systems of Differential Equations / Transforming Differential Equations / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 6. ADVANCED DIFFERENTIAL EQUATIONS Functions and Differential Equations / Sequences and Series / Taylor Series / Numerical Methods for Differential Equations / Stiff Differential Equations / Vector Equations / Boundary Value Problems / Equations with Variable Coefficients / Bessel and Legendre Equations / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 7. APPROXIMATION OF FUNCTIONS Polynomial Interpolation / Interpolation by Spline Functions / Least-Squares Curve Fitting / Orthogonal Functions / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 8. FOURIER ANALYSIS Fourier Series / Properties of Fourier Series / Fourier Transforms / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 9. LAPLACE TRANSFORMS Definition and Properties of the Laplace Transform / Computation of Inverse Laplace Transforms / MATLAB and Laplace Transforms / Applications to Differential Equations / Applications of Laplace Transforms to Linear Systems / Relationship of Fourier and Laplace Transforms / Summary of Laplace Transform Properties / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 10. DISCRETE SYSTEMS Introduction to the Sequences and Discrete Functions / Linear Difference Equations / Approximation to Differential Equations / Smoothing and Digital Filters / Introduction to z-Transforms / MATLAB Commands for Discrete Systems / z-Transform Solution of Difference Equations / Applications of z-transforms to Linear Discrete Systems / Frequency Response and Fourier Analysis / Summary of z-transform Properties / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 11. THE DISCRETE FOURIER TRANSFORM AND THE FFT Frequency Analysis of Signals / Discrete and Fast Fourier Transforms / MATLAB Fourier Commands / Practical Signal Analysis / Practical Signal Sampling and DFT Errors / Analysis of DFT for Computation (Optional) / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 12. ADVANCED CALCULUS Functions of Several Variables / Derivatives of a Multivariate Function / Differentials and Linear Approximation / Two-Dimensional Taylor Series / MATLAB Two-Dimensional Interpolation / MATLAB Differentiation / Extrema of Real-Valued Functions / Constrained Extrema and Lagrange Multipliers / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 13. VECTOR DIFFERENTIAL OPERATORS Vector and Scalar Fields / MATLAB Commands for Vector Differential Calculus / Directional Derivatives and the Gradient / The Divergence / The Curl / The Laplacian and Laplace''''s Equation / Vector Field Theory / Physical Application and Interpretation / Curvilinear Coordinates / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 14. VECTOR INTEGRAL CALCULUS Integration / Applications of Single Integrals / Double and Triple Integrals / Change of Variables in Double Integrals / Change of Variables in Triple Integrals / Applications of Multiple Integrals / MATLAB Commands for Integration / Line Integrals / Surface Integrals / Theorems of Vector Integral Calculus / Applications of Vector Field Theory / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers 15. PARTIAL DIFFERENTIAL EQUATIONS Introduction to Partial Differential Equations / Laplace''''s Equation / The Heat Equation / The Wave Equation / Reinforcement Exercises and Exploration Problems / Annotated Bibliography / Answers / INDEX / INDEX OF MATLAB COMMANDS

Editorial Reviews

Presents mathematical techniques for applications in engineering, physics, and applied mathematics. The major topics are vector and matrix algebra, differential equations, Fourier and Laplace analysis, discrete systems and discrete Fourier transforms, advanced calculus, and partial differential equations. Analytical and computer solutions to problems are integrated to clarify advanced mathematical techniques and abundant examples are used showing applications of mathematical principles using numerical and symbolic computer solutions. Requires a background in calculus and basic physics and some programming experience in a high level language. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Booknews