A Matlab Companion For Multivariable Calculus Book

	Preface	ix
	List of mfiles	xv
1	Basic MATLAB: The Command Line	1
1.1	First steps	1
1.2	Vectors and matrices	3
1.3	Array operations	6
1.4	Matrix multiplication and linear systems	8
1.5	MATLAB functions	10
1.6	Symbolic calculations	12
1.7	Two-dimensional graphs	16
1.8	Managing the workspace and getting help	19
2	Basic MATLAB: mfiles	21
2.1	Creating and editing files in MATLAB	21
2.2	Mfiles	22
2.3	Function functions	24
2.4	Script mfiles	25
2.5	MATLAB documents	27
3	Vectors, Lines, and Planes	33
3.1	Vectors	33
3.2	Plotting lines in two- and three-dimensional space	35
3.3	Planes	37
3.4	Viewing three-dimensional graphs	41
4	Curves in Space	47
4.1	Parametric representation of curves	47
4.2	Tangent vectors and velocity	49
4.3	Arc length	54
4.4	The geometry of curves	56
4.5	Rotations in the plane	59
4.6	Numerical differentiation	61
5	Functions of Two Variables	69
5.1	Defining numerical functions of several variables	69
5.2	Graphing numerical functions of two variables	70
5.3	Level curves	76
5.4	Graphing techniques for symbolically defined functions	78
5.5	Partial derivatives and the directional derivative	79
5.6	The gradient vector and level curves	83
5.7	The tangent plane approximation	86
5.8	More about colormaps	89
5.9	Cutting off a graph	90
5.10	The subplot command	93
6	Functions of Three Variables and Parametric Surfaces	101
6.1	Level sets and surfaces	101
6.2	Color slices of a solid	105
6.3	The gradient vector field	108
6.4	Parametric representation of surfaces	110
6.5	Normal vectors and tangent planes in parametric form	118
7	Solving Equations	123
7.1	Symbolic solutions	123
7.2	Numerical solutions in one dimension	125
7.3	Solving a single equation in two variables	128
7.4	Newton's method in two dimensions	130
8	Optimization	141
8.1	Critical points and the second-derivative test	141
8.2	Estimating the maximum and minimum	147
8.3	Constrained maximum and minimum problems	153
8.4	Functions of three variables	157
9	Multiple Integrals	169
9.1	Double integrals over rectangles	169
9.2	Nonrectangular regions of integration	177
9.3	Change of variable in double integrals	179
9.4	Triple integrals	188
10	Scalar Integrals Over Curves and Surfaces	197
10.1	Scalar integrals along curves	197
10.2	Scalar integrals on surfaces	199
10.3	Integrals over surfaces given parametrically	201
10.4	Surfaces composed of triangles	203
11	Integrals of Vector Fields Over Curves and Surfaces	219
11.1	Vector fields	219
11.2	Line integrals	223
11.3	Curl and Green's theorem	227
11.4	Flux integrals	232
11.5	The divergence theorem	234
12	Problems from Electrostatics and Fluid Flow	241
12.1	An important tool	241
12.2	Electrostatics	242
12.3	The geometry of fluid flow	247
12.4	The Euler equations	254
12.5	Incompressible flow	257
13	More Features of MATLAB	271
13.1	Data classes	271
13.2	The command feval	274
13.3	Vectorizing computations	275
13.4	Programming	276
Appendix	Instructor Demos	279
	Solutions to Selected Exercises	281
	Index	291