The Student's Introduction to MATHEMATICA ®: A Handbook for Precalculus, Calculus, and Linear Algebra

by Bruce F. Torrence , Eve A. Torrence

• ISBN13: 9780521717892
• ISBN10: 0521717892
• Edition: 2nd
• Format: Paperback
• Copyright: 2009-02-02
• Publisher: Cambridge University Press

Summary

The unique feature of this compact student's introduction is that it presents concepts in an order that closely follows a standard mathematics curriculum, rather than structure the book along features of the software. As a result, the book provides a brief introduction to those aspects of the Mathematica software program most useful to students. The second edition of this well loved book is completely rewritten for Mathematica 6 including coverage of the new dynamic interface elements, several hundred exercises and a new chapter on programming. This book can be used in a variety of courses, from precalculus to linear algebra. Used as a supplementary text it will aid in bridging the gap between the mathematics in the course and Mathematica. In addition to its course use, this book will serve as an excellent tutorial for those wishing to learn Mathematica and brush up on their mathematics at the same time.

Table of Contents

Preface	p. ix
Getting Started	p. 1
Launching Mathematica
The Basic Technique for Using Mathematica
The First Computation
Commands for Basic Arithmetic
Input and Output
The BasicMathInput Palette
Decimal In, Decimal Out
Use Parentheses to Group Terms
Three Well-Known Constants
Typing Commands in Mathematica
Saving Your Work and Quitting Mathematica
Frequently Asked Questions About Mathematica's Syntax
Working with Mathematica	p. 27
Opening Saved Notebooks
Adding Text to Notebooks
Printing
Creating Slide Shows
Creating Web Pages
Converting a Notebook to Another Format
Mathematica's Kernel
Tips for Working Effectively
Getting Help from Mathematica
Loading Packages
Troubleshooting
Functions and Their Graphs	p. 51
Defining a Function
Plotting a Function
Using Mathematica's Plot Options
Investigating Functions with Manipulate
Producing a Table of Values
Working with Piecewise Defined Functions
Plotting Implicitly Defined Functions
Combining Graphics
Enhancing Your Graphics
Working with Data
Managing Data-An Introduction to Lists
Importing Data
Working with Difference Equations
Algebra	p. 147
Factoring and Expanding Polynomials
Finding Roots of Polynomials with Solve and NSolve
Solving Equations and Inequalities with Reduce
Understanding Complex Output
Working with Rational Functions
Working with Other Expressions
Solving General Equations
Solving Difference Equations
Solving Systems of Equations
Calculus	p. 195
Computing Limits
Working with Difference Quotients
The Derivative
Visualizing Derivatives
Higher Order Derivatives
Maxima and Minima
Inflection Points
Implicit Differentiation
Differential Equations
Integration
Definite and Improper Integrals
Numerical Integration
Surfaces of Revolution
Sequences and Series
Multivariable Calculus	p. 251
Vectors
Real Valued Functions of Two or More Variables
Parametric Curves and Surfaces
Other Coordinate Systems
Vector Fields
Line Integrals and Surface Integrals
Linear Algebra	p. 335
Matrices
Performing Gaussian Elimination
Matrix Operations
Minors and Cofactors
Working with Large Matrices
Solving Systems of Linear Equations
Vector Spaces
Eigenvalues and Eigenvectors
Visualizing Linear Transformations
Programming	p. 385
Introduction
Fullform: What the Kernel Sees
Numbers
Map and Function
Control Structures and Looping
Scoping Constructs: With and Module
Iterations: Nest and Fold
Patterns
Solutions to Exercises www.studentsmathematica.com
Index	p. 461
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