Matlab Companion for Multivariable Calculus

ISBN-10: 012187625X
ISBN-13: 9780121876258
Edition: 2001
Authors: Jeffery Cooper
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Description: Beginning with a brief introduction to MatLab, this text covers graphing of curves and surfaces in two and three dimensions, laying the groundwork for further MatLab use.

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Book details

List price: $56.95
Copyright year: 2001
Publisher: Elsevier Science & Technology Books
Publication date: 12/18/2000
Binding: Paperback
Pages: 294
Size: 7.50" wide x 9.25" long x 0.50" tall
Weight: 1.100

Beginning with a brief introduction to MatLab, this text covers graphing of curves and surfaces in two and three dimensions, laying the groundwork for further MatLab use.

Preface
List of mfiles
Basic MATLAB: The Command Line
First steps
Vectors and matrices
Array operations
Matrix multiplication and linear systems
MATLAB functions
Symbolic calculations
Two-dimensional graphs
Managing the workspace and getting help
Basic MATLAB: mfiles
Creating and editing files in MATLAB
Mfiles
Function functions
Script mfiles
MATLAB documents
Vectors, Lines, and Planes
Vectors
Plotting lines in two- and three-dimensional space
Planes
Viewing three-dimensional graphs
Curves in Space
Parametric representation of curves
Tangent vectors and velocity
Arc length
The geometry of curves
Rotations in the plane
Numerical differentiation
Functions of Two Variables
Defining numerical functions of several variables
Graphing numerical functions of two variables
Level curves
Graphing techniques for symbolically defined functions
Partial derivatives and the directional derivative
The gradient vector and level curves
The tangent plane approximation
More about colormaps
Cutting off a graph
The subplot command
Functions of Three Variables and Parametric Surfaces
Level sets and surfaces
Color slices of a solid
The gradient vector field
Parametric representation of surfaces
Normal vectors and tangent planes in parametric form
Solving Equations
Symbolic solutions
Numerical solutions in one dimension
Solving a single equation in two variables
Newton's method in two dimensions
Optimization
Critical points and the second-derivative test
Estimating the maximum and minimum
Constrained maximum and minimum problems
Functions of three variables
Multiple Integrals
Double integrals over rectangles
Nonrectangular regions of integration
Change of variable in double integrals
Triple integrals
Scalar Integrals Over Curves and Surfaces
Scalar integrals along curves
Scalar integrals on surfaces
Integrals over surfaces given parametrically
Surfaces composed of triangles
Integrals of Vector Fields Over Curves and Surfaces
Vector fields
Line integrals
Curl and Green's theorem
Flux integrals
The divergence theorem
Problems from Electrostatics and Fluid Flow
An important tool
Electrostatics
The geometry of fluid flow
The Euler equations
Incompressible flow
More Features of MATLAB
Data classes
The command feval
Vectorizing computations
Programming
Instructor Demos
Solutions to Selected Exercises
Index

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