A Matlab Companion for Multivariable Calculus by Jeffery Cooper
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About this book :-
A Matlab Companion for Multivariable Calculus written by
Jeffery Cooper.
Multivariable calculus is an essential part of the mathematical education of scientists and engineers. In the past we relied almost entirely on chalk and blackboard, and examples that could be done by hand, to convey the key concepts of the subject. Now the advent of powerful, convenient software makes it imperative to reconsider how we teach multivariable calculus. In my opinion, the greatest impact of software is in the areas of graphics and computation.
Color graphics makes it possible to display curves, surfaces, and solids in two and three dimensions in a way that is both more effective and more engaging for the student. This is especially important for today’s students, who have not had much experience with solid geometry. Color can also be used as a fourth dimension to help locate extreme points, and to display quantities such as temperature, density, and fluid velocity.
Software also allows us to deal seriously with computation. Traditionally there has been an unnatural division of analysis and computation into separate compartments of mathematics. The paper-and-pencil exercises of the typical third-semester calculus text give valuable experience in manipulating symbols, but they are often quite contrived. Problems involving arc length, surface, and volume that can be done by hand are too limited in application and give the unfortunate impression that mathematicians are interested only in clever solutions of special problems and prefer to leave practical problems to engineers.
Book Detail :-
Title: A Matlab Companion for Multivariable Calculus
Edition:
Author(s): Jeffery Cooper
Publisher: Academic Press
Series:
Year: 2001
Pages: 311
Type: PDF
Language: English
ISBN: 012187625X,9780121876258,9780080489360
Country: USA
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About Author :-
Jeffery Cooper is Professor Emeritus, Mathematics Department,
The University of Maryland and author of "A Matlab Companion for Multivariable Calculus"
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Book Contents :-
A Matlab Companion for Multivariable Calculus written by
Jeffery Cooper
cover the following topics.
'
Preface
List of mfiles
1. Basic MATLAB: The Command Line
1.1 First steps
1.2 Vectors and matrices
1.3 Array operations
1.4 Matrix multiplication and linear systems
1.5 MATLAB functions
1.6 Symbolic calculations
1.7 Two-dimensional graphs
1.8 Managing the workspace and getting help
2. Basic MATLAB: mfiles
2.1 Creating and editing files in MATLAB
2.2 Mfiles
2.3 Function functions
2.4 Script mfiles
2.5 MATLAB documents
3. Vectors, Lines, and Planes
3.1 Vectors
3.2 Plotting lines in two- and three-dimensional space
3.3 Planes
3.4 Viewing three-dimensional graphs
4. Curves in Space
4.1 Parametric representation of curves
4.2 Tangent vectors and velocity
4.3 Arc length
4.4 The geometry of curves
4.5 Rotations in the plane
4.6 Numerical differentiation
5. Functions of Two Variables
5.1 Defining numerical functions of several variables
5.2 Graphing numerical functions of two variables
5.3 Level curves
5.4 Graphing techniques for symbolically defined functions
5.5 Partial derivatives and the directional derivative
5.6 The gradient vector and level curves
5.7 The tangent plane approximation
5.8 More about colormaps
5.9 Cutting off a graph
5.10 The subplot command
6. Functions of Three Variables and Parametric Surfaces
6.1 Level sets and surfaces
6.2 Color slices of a solid
6.3 The gradient vector field
6.4 Parametric representation of surfaces
6.5 Normal vectors and tangent planes in parametric form
7. Solving Equations
7.1 Symbolic solutions
7.2 Numerical solutions in one dimension
7.3 Solving a single equation in two variables
7.4 Newton’s method in two dimensions
8. Optimization
8.1 Critical points and the second-derivative test
8.2 Estimating the maximum and minimum
8.3 Constrained maximum and minimum problems
8.4 Functions of three variables
9. Multiple Integrals
9.1 Double integrals over rectangles
9.2 Nonrectangular regions of integration
9.3 Change of variable in double integrals
9.4 Triple integrals
10. Scalar Integrals Over Curves and Surfaces
10.1 Scalar integrals along curves
10.2 Scalar integrals on surfaces
10.3 Integrals over surfaces given parametrically
10.4 Surfaces composed of triangles
11. Integrals of Vector Fields Over Curves and Surfaces
11.1 Vector fields
11.2 Line integrals
11.3 Curl and Green’s theorem
11.4 Flux integrals
11.5 The divergence theorem
12. Problems from Electrostatics and Fluid Flow
12.1 An important tool
12.2 Electrostatics
12.3 The geometry of fluid flow
12.4 The Euler equations
12.5 Incompressible flow
13. More Features of MATLAB
13.1 Data classes
13.2 The command feval
13.3 Vectorizing computations
13.4 Programming
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