Mathematica by Example 3rd Edition

This book introduces the essentials of Mathematica. The examples and excercises presented are taken from algebra, trigonometry, and calculus topics that you are familiar with to assist you in becoming acquainted with Mathematica.


CONTENTS

1. Getting Started
Introduction to Mathematica
Getting Started with Mathematica
Five Basic Rules of Mathematica Syntax
Loading Packages
Getting Help from Mathematica


2. Basic Operations on Numbers, Expressions, and Functions
Built-in Constants
Built-in Functions
Expressions and Functions: Elementary Algebra
Basic Algebraic Operations on Expressions
Naming and Evaluating Expressions
Defining and Evaluating Functions
Graphing Functions, Expressions, and Equations
Functions of a Single Variable
Parametric and Polar Plots in Two Dimensions
Three-Dimensional and Contour Plots; Graphing Equations
Solving Equations
Exact Solutions of Equations
Approximate Solutions of Equations


3. Calculus
Limits
Using Graphs and Tables to Predict Limits
Computing Limits
One-Sided Limits
Differential Calculus
Definition of the Derivative
Calculating Derivatives
Implicit Differentiation
Tangent Lines
The First Derivative Test and Second Derivative Test
Applied Max/Min Problems
Antidifferentiation
Integral Calculus
Area
The Definite Integral
Approximating Definite Integrals
Area
Arc Length
Solids of Revolution
Series
Introduction to Sequences and Series
Convergence Tests
Alternating Series
Power Series
Taylor and Maclaurin Series
Taylor's Theorem
Other Series
Multivariable Calculus
Limits of Functions of Two Variables
Partial and Directional Derivatives
Iterated Integrals


4. Introduction to Lists and Tables
Lists and List Operations
Defining Lists
Plotting Lists of Points
Manipulating Lists: More on Part and Map
More on Graphing Lists; Graphing Lists of Points Using Graphics Primitives
Miscellaneous List Operations
Mathematics of Finance
Compound Interest
Future Value
Annuity Due
Present Value
Deferred Annuities
Amortization
More on Financial Planning
Other Applications
Approximating Lists with Functions
Introduction to Fourier Series
The Mandelbrot Set and Julia Sets


5. Matrices and Vectors: Topics from Linear Algebra and Vector Calculus
Nested Lists: Introduction to Matrices, Vectors, and Matrix Operations
Defining Nested Lists, Matrices, and Vectors
Extracting Elements of Matrices
Basic Computations with Matrices
Basic Computations with Vectors
Linear Systems of Equations
Calculating Solutions of Linear Systems of Equations
Gauss-Jordan Elimination
Selected Topics from Linear Algebra
Fundamental Subspaces Associated with Matrices
The Gram-Schmidt Process
Linear Transformations
Eigenvalues and Eigenvectors
Jordan Canonical Form
The QR Method
Maxima and Minima Using Linear Programming
The Standard Form of a Linear Programming Problem
The Dual Problem
Selected Topics from Vector Calculus
Vector-Valued Functions
Line Integrals
Surface Integrals
A Note on Nonorientability


6. Applications Related to Ordinary and Partial Differential Equations
First-Order Differential Equations
Seperable Equations
Linear Equations
Nonlinear Equations
Numerical Methods
Second-Order Linear Equations
Basic Theory
Constant Coefficients
Undetermined Coefficients
Variation of Parameters
Higher-Order Linear Equations
Basic Theory
Constant Coefficients
Undetermined Coefficients
Laplace Transform Methods
Nonlinear Higher-Order Equations
Systems of Equations
Linear Systems
Nonhomogeneous Linear Systems
Nonlinear Systems
Some Partial Differential Equations 6.5.1 The One-Dimensional Wave Equation
The Two-Dimensional Wave Equation
Other Partial Differential Equations