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Elements of Matrix Modeling and Computing with MATLAB

Publisher: 
Chapman & Hall/CRC
Number of Pages: 
402
Price: 
79.95
ISBN: 
1584886277

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.

Date Received: 
Friday, October 27, 2006
Reviewable: 
Yes
Include In BLL Rating: 
No
Robert E. White
Publication Date: 
2007
Format: 
Hardcover
Category: 
Textbook
Henry Ricardo
02/4/2007

 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

Publish Book: 
Modify Date: 
Thursday, February 22, 2007

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