Designed for a course in multivariable calculus, this book provides a collection of MATLAB programs and exercises, along with basic concepts, computations, and graphics. Chapters focus on the command line, mfiles, vectors, curves, functions of two and three variables, solving equations, optimization, multiple integrals, scalar integrals, and electrostasis and fluid flow, Exercises include applications to economics, physics, engineering, and biology. Cooper teaches mathematics at the University of Maryland.
Author(s): Jeffery Cooper
Edition: 1st
Publisher: Academic Press
Year: 2001
Language: English
Pages: 311
A MATLAB® Companion for Multivariable Calculus......Page 3
Copyright Page......Page 4
Contents......Page 6
Preface......Page 10
List of mfiles......Page 16
1.1 First steps......Page 18
1.2 Vectors and matrices......Page 20
1.3 Array operations......Page 23
1.4 Matrix multiplication and linear systems......Page 25
1.5 MATLAB functions......Page 27
1.6 Symbolic calculations......Page 29
1.7 Two-dimensional graphs......Page 33
1.8 Managing the workspace and getting help......Page 36
2.1 Creating and editing mfiles in MATLAB......Page 38
2.2 Mfiles......Page 39
2.3 Function functions......Page 41
2.4 Script mfiles......Page 42
2.5 MATLAB documents......Page 44
3.1 Vectors......Page 50
3.2 Plotting lines in two- and three-dimensional space......Page 52
3.3 Planes......Page 54
3.4 Viewing three-dimensional graphs......Page 58
4.1 Parametric representation of curves......Page 64
4.2 Tangent vectors and velocity......Page 66
4.3 Arc length......Page 71
4.4 The geometry of curves......Page 73
4.5 Rotations in the plane......Page 76
4.6 Numerical differentiation......Page 78
5.1 Defining numerical functions of several variables......Page 86
5.2 Graphing numerical functions of two variables......Page 87
5.3 Level curves......Page 93
5.4 Graphing techniques for symbolically defined functions......Page 95
5.5 Partial derivatives and the directional derivative......Page 96
5.6 The gradient vector and level curves......Page 100
5.7 The tangent plane approximation......Page 103
5.8 More about colormaps......Page 106
5.9 Cutting off a graph......Page 107
5.10 The subplot command......Page 110
6.1 Level sets and surfaces......Page 118
6.2 Color slices of a solid......Page 122
6.3 The gradient vector field......Page 125
6.4 Parametric representation of surfaces......Page 127
6.5 Normal vectors and tangent planes in parametric form......Page 135
7.1 Symbolic solutions......Page 140
7.2 Numerical solutions in one dimension......Page 142
7.3 Solving a single equation in two variables......Page 145
7.4 Newton’s method in two dimensions......Page 147
8.1 Critical points and the second-derivative test......Page 158
8.2 Estimating the maximum and minimum......Page 164
8.3 Constrained maximum and minimum problems......Page 170
8.4 Functions of three variables......Page 174
9.1 Double integrals over rectangles......Page 186
9.2 Nonrectangular regions of integration......Page 194
9.3 Change of variable in double integrals......Page 196
9.4 Triple integrals......Page 205
10.1 Scalar integrals along curves......Page 214
10.2 Scalar integrals on surfaces......Page 216
10.3 Integrals over surfaces given parametrically......Page 218
10.4 Surfaces composed of triangles......Page 220
11.1 Vector fields......Page 236
11.2 Line integrals......Page 240
11.3 Curl and Green’s theorem......Page 244
11.4 Flux integrals......Page 249
11.5 The divergence theorem......Page 251
12.1 An important tool......Page 258
12.2 Electrostatics......Page 259
12.3 The geometry of fluid flow......Page 264
12.4 The Euler equations......Page 271
12.5 Incompressible flow......Page 274
13.1 Data classes......Page 288
13.2 The command feval......Page 291
13.3 Vectorizing computations......Page 292
13.4 Programming......Page 293
Appendix: Instructor Demos......Page 296
Solutions to Selected Exercises......Page 298
Index......Page 308
