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The Student's Introduction to MATHEMATICA ? Second Edition

Book Description

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

  1. Cover
  2. Title
  3. Copyright
  4. Dedication
  5. Contents
  6. Preface
  7. 1 Getting Started
    1. Launching Mathematica
    2. The Basic Technique for Using Mathematica
    3. The First Computation
    4. Commands for Basic Arithmetic
    5. Input and Output
    6. The BasicMathInput Palette
    7. Decimal In, Decimal Out
    8. Use Parentheses to Group Terms
    9. Three Well-Known Constants
    10. Typing Commands in Mathematica
    11. Saving Your Work and Quitting Mathematica
    12. Frequently Asked Questions About Mathematica’s Syntax
  8. 2 Working with Mathematica
    1. Opening Saved Notebooks
    2. Adding Text to Notebooks
    3. Printing
    4. Creating Slide Shows
    5. Creating Web Pages
    6. Converting a Notebook to Another Format
    7. Mathematica’s Kernel
    8. Tips for Working Effectively
    9. Getting Help from Mathematica
    10. Loading Packages
    11. Troubleshooting
  9. 3 Functions and Their Graphs
    1. Defining a Function
    2. Plotting a Function
    3. Using Mathematica’s Plot Options
    4. Investigating Functions with Manipulate
    5. Producing a Table of Values
    6. Working with Piecewise Defined Functions
    7. Plotting Implicitly Defined Functions
    8. Combining Graphics
    9. Enhancing Your Graphics
    10. Working with Data
    11. Managing Data—An Introduction to Lists
    12. Importing Data
    13. Working with Difference Equations
  10. 4 Algebra
    1. Factoring and Expanding Polynomials
    2. Finding Roots of Polynomials with Solve and NSolve
    3. Solving Equations and Inequalities with Reduce
    4. Understanding Complex Output
    5. Working with Rational Functions
    6. Working with Other Expressions
    7. Solving General Equations
    8. Solving Difference Equations
    9. Solving Systems of Equations
  11. 5 Calculus
    1. Computing Limits
    2. Working with Difference Quotients
    3. The Derivative
    4. Visualizing Derivatives
    5. Higher Order Derivatives
    6. Maxima and Minima
    7. Inflection Points
    8. Implicit Differentiation
    9. Differential Equations
    10. Integration
    11. Definite and Improper Integrals
    12. Numerical Integration
    13. Surfaces of Revolution
    14. Sequences and Series
  12. 6 Multivariable Calculus
    1. Vectors
    2. Real-Valued Functions of Two or More Variables
    3. Parametric Curves and Surfaces
    4. Other Coordinate Systems
    5. Vector Fields
    6. Line Integrals and Surface Integrals
  13. 7 Linear Algebra
    1. Matrices
    2. Performing Gaussian Elimination
    3. Matrix Operations
    4. Minors and Cofactors
    5. Working with Large Matrices
    6. Solving Systems of Linear Equations
    7. Vector Spaces
    8. Eigenvalues and Eigenvectors
    9. Visualizing Linear Transformations
  14. 8 Programming
    1. Introduction
    2. FullForm: What the Kernel Sees
    3. Numbers
    4. Map and Function
    5. Control Structures and Looping
    6. Scoping Constructs: With and Module
    7. Iterations: Nest and Fold
    8. Patterns
  15. Index