A Physicist’s Guide to Mathematica

✍ Scribed by Patrick T. Tam

• Publisher: Academic Press is an Imprint of Elsevier
• Year: 2008
• Tongue: English
• Leaves: 749
• Edition: 2
• Category: Library

✦ Table of Contents

A Physicist’s Guide to Mathematica
Copyright Page
Contents
Preface to the Second Edition
Preface to the First Edition
Part I: Mathematica with Physics
Chapter 1. The First Encounter
1.1 The First Ten Minutes
1.2 A Touch of Physics
1.2.1 Numerical Calculations
1.2.2 Symbolic Calculations
1.2.3 Graphics
1.3 Online Help
1.4 Warning Messages
1.5 Packages
1.6 Notebook Interfaces
1.6.1 Notebooks
1.6.2 Entering Greek Letters
1.6.3 Getting Help
1.6.4 Preparing Input
1.6.5 Starting and Aborting Calculations
1.7 Problems
Chapter 2. Interactive Use of Mathematica
2.1 Numerical Capabilities
2.1.1 Arithmetic Operations
2.1.2 Spaces and Parentheses
2.1.3 Common Mathematical Constants
2.1.4 Some Mathematical Functions
2.1.5 Cases and Brackets
2.1.6 Ways to Refer to Previous Results
2.1.7 Standard Computations
2.1.8 Exact versus Approximate Values
2.1.9 Machine Precision versus Arbitrary Precision
2.1.10 Special Functions
2.1.11 Matrices
2.1.12 Double Square Brackets
2.1.13 Linear Least-Squares Fit
2.1.14 Complex Numbers
2.1.15 Random Numbers
2.1.16 Numerical Solution of Polynomial Equations
2.1.17 Numerical Integration
2.1.18 Numerical Solution of Differential Equations
2.1.19 Iterators
2.1.20 Exercises
2.2 Symbolic Capabilities
2.2.1 Transforming Algebraic Expressions
2.2.2 Transforming Trigonometric Expressions
2.2.3 Transforming Expressions Involving Special Functions
2.2.4 Using Assumptions
2.2.5 Obtaining Parts of Algebraic Expressions
2.2.6 Units, Conversion of Units, and Physical Constants
2.2.7 Assignments and Transformation Rules
2.2.8 Equation Solving
2.2.9 Differentiation
2.2.10 Integration
2.2.11 Sums
2.2.12 Power Series
2.2.13 Limits
2.2.14 Solving Differential Equations
2.2.15 Immediate versus Delayed Assignments and Transformation Rules
2.2.16 Defining Functions
2.2.17 Relational and Logical Operators
2.2.18 Fourier Transforms
2.2.19 Evaluating Subexpressions
2.2.20 Exercises
2.3 Graphical Capabilities
2.3.1 Two-Dimensional Graphics
2.3.2 Three-Dimensional Graphics
2.3.3 Interactive Manipulation of Graphics
2.3.4 Animation
2.3.5 Exercise
2.4 Lists
2.4.1 Defining Lists
2.4.2 Generating and Displaying Lists
2.4.3 Counting List Elements
2.4.4 Obtaining List and Sublist Elements
2.4.5 Changing List and Sublist Elements
2.4.6 Rearranging Lists
2.4.7 Restructuring Lists
2.4.8 Combining Lists
2.4.9 Operating on Lists
2.4.10 Using Lists in Computations
2.4.11 Analyzing Data
2.4.12 Exercises
2.5 Special Characters, Two-Dimensional Forms, and Format Types
2.5.1 Special Characters
2.5.2 Two-Dimensional Forms
2.5.3 Input and Output Forms
2.5.4 Exercises
2.6 Problems
Chapter 3. Programming in Mathematica
3.1 Expressions
3.1.1 Atoms
3.1.2 Internal Representation
3.1.3 Manipulation
3.1.4 Exercises
3.2 Patterns
3.2.1 Blanks
3.2.2 Naming Patterns
3.2.3 Restricting Patterns
3.2.4 Structural Equivalence
3.2.5 Attributes
3.2.6 Defaults
3.2.7 Alternative or Repeated Patterns
3.2.8 Multiple Blanks
3.2.9 Exercises
3.3 Functions
3.3.1 Pure Functions
3.3.2 Selecting a Definition
3.3.3 Recursive Functions and Dynamic Programming
3.3.4 Functional Iterations
3.3.5 Protection
3.3.6 Upvalues and Downvalues
3.3.7 Exercises
3.4 Procedures
3.4.1 Local Symbols
3.4.2 Conditionals
3.4.3 Loops
3.4.4 Named Optional Arguments
3.4.5 An Example: Motion of a Particle in One Dimension
3.4.6 Exercises
3.5 Graphics
3.5.1 Graphics Objects
3.5.2 Two-Dimensional Graphics
3.5.3 Three-Dimensional Graphics
3.5.4 Exercises
3.6 Programming Styles
3.6.1 Procedural Programming
3.6.2 Functional Programming
3.6.3 Rule-Based Programming
3.6.4 Exercises
3.7 Packages
3.7.1 Contexts
3.7.2 Context Manipulation
3.7.3 A Sample Package
3.7.4 Template for Packages
3.7.5 Exercises
Part II: Physics with Mathematica
Chapter 4. Mechanics
4.1 Falling Bodies
4.1.1 The Problem
4.1.2 Physics of the Problem
4.1.3 Solution with Mathematica
4.2 Projectile Motion
4.2.1 The Problem
4.2.2 Physics of the Problem
4.2.3 Solution with Mathematica
4.3 The Pendulum
4.3.1 The Problem
4.3.2 Physics of the Problem
4.3.3 Solution with Mathematica
4.4 The Spherical Pendulum
4.4.1 The Problem
4.4.2 Physics of the Problem
4.4.3 Solution with Mathematica
4.5 Problems
Chapter 5. Electricity and Magnetism
5.1 Electric Field Lines and Equipotentials
5.1.1 The Problem
5.1.2 Physics of the Problem
5.1.3 Solution with Mathematica
5.2 Laplace’s Equation
5.2.1 The Problem
5.2.2 Physics of the Problem
5.2.3 Solution with Mathematica
5.3 Charged Particle in Crossed Electric and Magnetic Fields
5.3.1 The Problem
5.3.2 Physics of the Problem
5.3.3 Solution with Mathematica
5.4 Problems
Chapter 6. Quantum Physics
6.1 Blackbody Radiation
6.1.1 The Problem
6.1.2 Physics of the Problem
6.1.3 Solution with Mathematica
6.2 Wave Packets
6.2.1 The Problem
6.2.2 Physics of the Problem
6.2.3 Solution with Mathematica
6.3 Particle in a One-Dimensional Box
6.3.1 The Problem
6.3.2 Physics of the Problem
6.3.3 Solution with Mathematica
6.4 The Square Well Potential
6.4.1 The Problem
6.4.2 Physics of the Problem
6.4.3 Solution with Mathematica
6.5 Angular Momentum
6.5.1 The Problem
6.5.2 Physics of the Problem
6.5.3 Solution with Mathematica
6.6 The Kronig–Penney Model
6.6.1 The Problem
6.6.2 Physics of the Problem
6.6.3 Solution with Mathematica
6.7 Problems
Appendices
A The Last Ten Minutes
B Operator Input Forms
C Solutions to Exercises
D Solutions to Problems
References
Index