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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: ** US

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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
**

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