Home Page Icon
Home Page
Table of Contents for
I. Mathematica with Physics
Close
I. Mathematica with Physics
by Patrick T. Tam
A Physicist's Guide to Mathematica, 2nd Edition
Copyright
Dedication
Preface to the Second Edition
Preface to the First Edition
Purpose
Uses
Organization
Suggestions
Prerequisites
Computer Systems
Acknowledgments
I. Mathematica with Physics
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
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
2.3.1.1. Basic Plots
2.3.1.2. Options
2.3.1.3. Multiple Plots
2.3.1.4. FindRoot
2.3.1.5. FindMinimum and FindMaximum
2.3.1.6. Data Plots
2.3.1.7. Parametric Plots
2.3.1.8. Interactive Graphics Drawing
2.3.2. Three-Dimensional Graphics
2.3.2.1. Surface Plots
2.3.2.2. Viewpoint
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
2.4.11.1. Basic Error Analysis
2.4.11.2. Nonlinear Least-Squares Fit
2.4.11.3. Interpolation
2.4.12. Exercises
2.5. Special Characters, Two-Dimensional Forms, and Format Types
2.5.1. Special Characters
2.5.1.1. Ways to Enter Special Characters
2.5.1.2. Letters and Letterlike Forms
2.5.1.3. Operators
Logical Operators
Bracketing Operators
Other Operators
2.5.1.4. Structural Elements and Spacing Characters
2.5.1.5. Similar-Looking Characters
2.5.2. Two-Dimensional Forms
2.5.2.1. Ways to Enter Two-Dimensional Forms
Palettes
Control Keys
Ordinary Characters
Create Table/Matrix
2.5.2.2. Some Two-Dimensional Forms with Built-in Meaning
2.5.2.3. Two-Dimensional Notation in Physics
2.5.3. Input and Output Forms
2.5.4. Exercises
2.6. Problems
3. Programming in Mathematica
3.1. Expressions
3.1.1. Atoms
3.1.2. Internal Representation
3.1.3. Manipulation
3.1.3.1. Obtaining Parts of Expressions
3.1.3.2. Changing Parts of Expressions
3.1.3.3. Rearranging Expressions
3.1.3.4. Restructuring Expressions
3.1.3.5. Operating on Expressions
3.1.3.6. Manipulating Equations
3.1.4. Exercises
3.2. Patterns
3.2.1. Blanks
3.2.2. Naming Patterns
3.2.3. Restricting Patterns
3.2.3.1. Types
3.2.3.2. Tests
3.2.3.3. Conditions
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
3.4.3.1. Changing Values of Variables
3.4.3.2. Do, While, and For
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
3.5.2.1. Two-Dimensional Graphics Primitives
3.5.2.2. Two-Dimensional Graphics Directives
3.5.2.3. Two-Dimensional Graphics Options
3.5.2.4. Wave Motion
3.5.3. Three-Dimensional Graphics
3.5.3.1. Three-Dimensional Graphics Primitives
3.5.3.2. Three-Dimensional Graphics Directives
3.5.3.3. Three-Dimensional Graphics Options
3.5.3.4. Crystal Structure
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
3.7.3.1. The Problem
3.7.3.2. The Package
3.7.3.3. Analysis of the Package
3.7.4. Template for Packages
3.7.5. Exercises
II. Physics with Mathematica
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
4.3.2.1. The Plane Pendulum
4.3.2.2. The Damped Pendulum
4.3.2.3. The Damped, Driven Pendulum
4.3.3. Solution with Mathematica
4.3.3.1. The Plane Pendulum
4.3.3.2. The Damped Pendulum
4.3.3.3. The Damped, Driven Pendulum
4.3.3.4. ChaoticPendulum’: A Mathematica Package
4.4. The Spherical Pendulum
4.4.1. The Problem
4.4.2. Physics of the Problem
4.4.3. Solution with Mathematica
4.4.3.1. θ0 = 120, 0 = 0, ϕ0 = 45, 0 = 0
4.4.3.2. θ0 = 135, 0 = 0, ϕ0 = 90, 0 = 21/4
4.4.3.3. θ0 = 135, 0 = 2.5, ϕ0 = 90, 0 = 1.5 ×21/4
4.4.3.4. θ0 = 120, 0 = 0.75, ϕ0 = 90, 0 = 2.0 × 21/4
4.5. Problems
5. Electricity and Magnetism
5.1. Electric Field Lines and Equipotentials
5.1.1. The Problem
5.1.2. Physics of the Problem
5.1.2.1. Electric Field Lines
5.1.2.2. Equipotentials
5.1.2.3. Electric Field Lines and Equipotentials for Two Point Charges
5.1.3. Solution with Mathematica
5.1.3.1. q1 = q2 = + q
5.1.3.2. q1 = +2q and q2 = –q
5.2. Laplace’s Equation
5.2.1. The Problem
5.2.2. Physics of the Problem
5.2.2.1. Analytical Solution
5.2.2.2. Numerical Solution
5.2.3. Solution with Mathematica
5.2.3.1. Analytical Solution
5.2.3.2. Numerical Solution
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
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
6.1.3.1. u(λ, T) at Several Temperatures
6.1.3.2. Wien’s Displacement Law
6.1.3.3. λmax for Solar Radiation
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
6.3.3.1. Function Definitions
6.3.3.2. Animation
6.4. The Square Well Potential
6.4.1. The Problem
6.4.2. Physics of the Problem
6.4.2.1. Analytical Solution
6.4.2.2. Numerical Solution
6.4.3. Solution with Mathematica
6.4.3.1. Analytical Solution
6.4.3.2. Numerical Solution
6.5. Angular Momentum
6.5.1. The Problem
6.5.2. Physics of the Problem
6.5.2.1. Angular Momentum in Quantum Mechanics
6.5.2.2. Orbital Angular Momentum
6.5.2.3. The Eigenvalue 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
A. The Last Ten Minutes
B. Operator Input Forms
C. Solutions to Exercises
Section 2.1.20
Section 2.2.20
Section 2.3.5
Section 2.4.12
Section 2.5.4
Section 3.1.4
Section 3.2.9
Section 3.3.7
Section 3.4.6
Section 3.5.4
Section 3.6.4
Section 3.7.5
D. Solutions to Problems
Section 1.7
Section 2.6
Section 4.5
Section 5.4
Section 6.7
References
Search in book...
Toggle Font Controls
Playlists
Add To
Create new playlist
Name your new playlist
Playlist description (optional)
Cancel
Create playlist
Sign In
Email address
Password
Forgot Password?
Create account
Login
or
Continue with Facebook
Continue with Google
Sign Up
Full Name
Email address
Confirm Email Address
Password
Login
Create account
or
Continue with Facebook
Continue with Google
Prev
Previous Chapter
Preface to the First Edition
Next
Next Chapter
1. The First Encounter
Part I.
Mathematica
with Physics
Add Highlight
No Comment
..................Content has been hidden....................
You can't read the all page of ebook, please click
here
login for view all page.
Day Mode
Cloud Mode
Night Mode
Reset