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Publisher:

Chapman & Hall/CRC

Publication Date:

2007

Number of Pages:

402

Format:

Hardcover

Price:

79.95

ISBN:

1584886277

Category:

Textbook

[Reviewed by , on ]

Henry Ricardo

02/4/2007

This book is meant to provide “math-on-time” for second-year students of science and engineering and is intended as the text for a two- or three-credit course concurrent with a second semester of calculus.

There are seven basic applications that provide motivation for the mathematics being illustrated: circuits, trusses, mixing tanks, heat conduction, data modeling, motion of a mass, and image filters. The mathematical tools needed to handle these applications are developed quickly. The reader is introduced to complex numbers and basic complex-valued functions, vectors and matrices, curve fitting, linear ordinary differential equations, Laplace and Fourier transform methods, and some computational methods. As is typical for such texts, the emphasis is more on skills than on theory. *MATLAB*^{®} is used as the main computing tool.

The twelve-item bibliography includes some standalone web sites and some URLs associated with referenced books. The link to the NASA Mars Rover site seems to be broken.

Although I sometimes cringe at attempts to cram more etiolated mathematical content into an engineering curriculum, I find that the book under review has some redeeming features. For example, data modeling is applied to some interesting examples — the influence of cross-border shopping on the price of goods, the effect of various home attributes (age, the number of bathrooms…) on real estate appraisal, and various population questions. Detailed *MATLAB*^{®} function and code files are provided for most applications. In addition to its intended use, this book might serve as a source of some examples/problems for a linear algebra, differential equations, or applied mathematics course.

Henry Ricardo (henry@mec.cuny.edu) is Professor of Mathematics at Medgar Evers College of The City University of New York and Secretary of the Metropolitan NY Section of the MAA. His book, A Modern Introduction to Differential Equations, was published by Houghton Mifflin in January, 2002; and he is currently writing a linear algebra text.

List of Figures

List of Tables

Preface

Introduction

VECTORS IN THE PLANE

Floating Point and Complex Numbers

Complex Valued Functions

Vectors in R2

Dot Product and Work

Lines and Curves in R2 and C

VECTORS IN SPACE

Vectors and Dot Product

Cross and Box Products

Lines and Curves in R3

Planes in R3

Extensions to Rn

Ax = d: UNIQUE SOLUTION

Matrix Models

Matrix Products

Special Cases of Ax = d

Row Operations and Gauss Elimination

Inverse Matrices

LU Factorization

Determinants and Cramer's Rule

Ax = d: LEAST SQUARES SOLUTION

Curve Fitting to Data

Normal Equations

Multilinear Data Fitting

Parameter Identification

Ax = d: MULTIPLE SOLUTIONS

Subspaces and Solutions in R3

Row Echelon Form

Nullspaces and Equilibrium Equations

LINEAR INITIAL VALUE PROBLEMS

First Order Linear

Second Order Linear

Homogeneous and Complex Solution

Nonhomogeneous Linear Differential Equations

System Form of Linear Second Order

EIGENVALUES AND DIFFERENTITAL EQUATIONS

Solution of x' = Ax by Elimination

Real Eigenvalues and Eigenvectors

Solution of x' = Ax + f (t)

IMAGE PROCESSING IN THE SPACE DOMAIN

Matrices and Images

Contrast and Histograms

Blurring and Sharpening

IMAGE PROCESSING IN THE FREQUENCY DOMAIN

Laplace and Fourier Transforms

Properties of DFT

DFT in Rn × Rn

Frequency Filters in Rn × Rn

Appendix: Solutions to Odd Exercises

Bibliography

Index

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