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A Matlab Companion for Multivariable Calculus - Jeffery Cooper

A Matlab Companion for Multivariable Calculus

Paperback

Published: 1st December 2000
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Offering a concise collection of MatLab programs and exercises to accompany a third semester course in multivariable calculus, "A MatLab Companion for Multivariable Calculus" introduces simple numerical procedures such as numerical differentiation, numerical integration and Newton's method in several variables, thereby allowing students to tackle realistic problems. The many examples show students how to use MatLab effectively and easily in many contexts. Numerous exercises in mathematics and applications areas are presented, graded from routine to more demanding projects requiring some programming. Matlab M-files are provided on the Harcourt/Academic Press web site at http: //www.harcourt-ap.com/matlab.html.
* Computer-oriented material that complements the essential topics in multivariable calculus
* Main ideas presented with examples of computations and graphics displays using MATLAB
* Numerous examples of short code in the text, which can be modified for use with the exercises
* MATLAB files are used to implement graphics displays and contain a collection of mfiles which can serve as demos

Excerpts from the reviews: "This text does a good job of explaining how MATLAB works at exactly the appropriate level. The use of MATLAB also encourages students toward more numerical thinking than do the packages that are primarily symbolic manipulations."

"The author's writing is very clear. Students should find it pleasant reading, as I did."

"I liked the problems. They presented the main issues and calculations from a variety of angles, so that students have to think and learn on almost all of them."

"I like the serious applications at the end-to fluids, for example: this would also be helpful for nice demonstrations which the instructor could do in class."

"My favorite aspect of this text is that by using MATLAB it naturally incorporates more numerical thinking into Multivariable Calculus. This builds on recent trends in Single-Variable Calculus 'reform'."

Prefacep. ix
List of mfilesp. xv
Basic MATLAB: The Command Linep. 1
First stepsp. 1
Vectors and matricesp. 3
Array operationsp. 6
Matrix multiplication and linear systemsp. 8
MATLAB functionsp. 10
Symbolic calculationsp. 12
Two-dimensional graphsp. 16
Managing the workspace and getting helpp. 19
Basic MATLAB: mfilesp. 21
Creating and editing files in MATLABp. 21
Mfilesp. 22
Function functionsp. 24
Script mfilesp. 25
MATLAB documentsp. 27
Vectors, Lines, and Planesp. 33
Vectorsp. 33
Plotting lines in two- and three-dimensional spacep. 35
Planesp. 37
Viewing three-dimensional graphsp. 41
Curves in Spacep. 47
Parametric representation of curvesp. 47
Tangent vectors and velocityp. 49
Arc lengthp. 54
The geometry of curvesp. 56
Rotations in the planep. 59
Numerical differentiationp. 61
Functions of Two Variablesp. 69
Defining numerical functions of several variablesp. 69
Graphing numerical functions of two variablesp. 70
Level curvesp. 76
Graphing techniques for symbolically defined functionsp. 78
Partial derivatives and the directional derivativep. 79
The gradient vector and level curvesp. 83
The tangent plane approximationp. 86
More about colormapsp. 89
Cutting off a graphp. 90
The subplot commandp. 93
Functions of Three Variables and Parametric Surfacesp. 101
Level sets and surfacesp. 101
Color slices of a solidp. 105
The gradient vector fieldp. 108
Parametric representation of surfacesp. 110
Normal vectors and tangent planes in parametric formp. 118
Solving Equationsp. 123
Symbolic solutionsp. 123
Numerical solutions in one dimensionp. 125
Solving a single equation in two variablesp. 128
Newton's method in two dimensionsp. 130
Optimizationp. 141
Critical points and the second-derivative testp. 141
Estimating the maximum and minimump. 147
Constrained maximum and minimum problemsp. 153
Functions of three variablesp. 157
Multiple Integralsp. 169
Double integrals over rectanglesp. 169
Nonrectangular regions of integrationp. 177
Change of variable in double integralsp. 179
Triple integralsp. 188
Scalar Integrals Over Curves and Surfacesp. 197
Scalar integrals along curvesp. 197
Scalar integrals on surfacesp. 199
Integrals over surfaces given parametricallyp. 201
Surfaces composed of trianglesp. 203
Integrals of Vector Fields Over Curves and Surfacesp. 219
Vector fieldsp. 219
Line integralsp. 223
Curl and Green's theoremp. 227
Flux integralsp. 232
The divergence theoremp. 234
Problems from Electrostatics and Fluid Flowp. 241
An important toolp. 241
Electrostaticsp. 242
The geometry of fluid flowp. 247
The Euler equationsp. 254
Incompressible flowp. 257
More Features of MATLABp. 271
Data classesp. 271
The command fevalp. 274
Vectorizing computationsp. 275
Programmingp. 276
Instructor Demosp. 279
Solutions to Selected Exercisesp. 281
Indexp. 291
Table of Contents provided by Syndetics. All Rights Reserved.

ISBN: 9780121876258
ISBN-10: 012187625X
Audience: General
Format: Paperback
Language: English
Number Of Pages: 294
Published: 1st December 2000
Publisher: ACADEMIC PR INC
Country of Publication: US
Dimensions (cm): 25.4 x 17.81  x 1.65
Weight (kg): 0.54