Table of Contents/Index

Nicholas Wheeler

I provide here a list—in order of appearance—of the topics and commands presented in the 3rd edition (2007) of the six manuals that comprise PHYSICIST'S INTRODUCTION OF MATHEMATICA 6.

Laboratory 0

Why Bother to Learn Mathematica?

Getting Started...and Stopped

Timing

Terminating a Running Calculation

Notebooks

Input Techniques & Tips

Palettes

A Cautionary Warning

Creating 2-Dimensional Commands &  Special Symbols at the Keyboard

Three Flavors of =

Assignment

Delayed Assignment: Functional Definition

Piece-wise Functional Definition

Equality Tests

Special Flavors of =, and Some of its Relatives

Clear

How to Clear a Subscripted Variable

Sources of Information

Hardcopy Materials

Hyperlink

Built-in Sources

<<PhysicalConstants`

?Information
?Options

Your Own "My Tricks" Notebook

Memory Management

MaxMemoryUsed[]

Laboratory 1

Basic Graphics

Basic Resources

Simple 2-Dimensional Plotting

?Plot
?Ticks
?Thickness
?AbsoluteThickness
?RGBColor
?Hue
?PlotRange

?Series

Filled Plots

Polar Plots

List Plots

?Fibonacci
?Table
?AxesOrigin

Parametruc Plots

3-Dimensional Plotting

?Plot3D
?Mesh

Spherical  Plots

ListPlot3D

Parametric Plot3D

2D Projections of 3S Surfaces

Density Plots

Contour Plots

Laboratory 2

More Advanced Graphics

Graphics Primitives

The Graphics Menu

?Arrow

Graphical Representation of Vector Fields

?Needs
?Get

Needs["VectorFieldPlots`"]

?VectorFieldPlot

?GradientFieldPlot
?HamiltonianFieldPlot

Polyhedra

Composite Figures

?GraphicsGrid
?Spacings

Exporting Graphics

Dynamic Display

Manipulate

Animation

Example: Motion of a Classical Oscillator

Example: 3D Animation

Audio

?Sound

Example: Non-acoustic Application of Audio

Needs["Music`"]

Laboratory 3

Some Useful Standard Packages

Physical Constants

Units Conversions

Calendar

Algebra

Short List of Basic Operations

?Together
?Apart
?Cancel
?ExpandDenominator
?ExpandNumerator

?FactorInteger

?Factor

Finding the Roots of a Polynomial

?Solve
?NSolve

The RootPlot Command

Solving Systems of Simultaneous Equations

Application to the Theory of One-dimensional Elastic Collisions

Trigonometry

?TrigExpand
?TrigFactor
?TrigReduce
?TrigToExp
?ExpToTrig

Matrices

Creating Matrices

Subscripts & Superscripts/Exponents

Some Common Matrix Operations

?Trace
?Det
?Transpose
?Inverse
?Dimensions
?MatrixPower
?MatrixExp

Application of a Sort that Arises in Connection with the Solution of Differential Equations

Characteristic Equation, Eigenvalues, Eigenvectors

?CharacteristicEquation
?Eigenvalues
?Eigenvectors
?Eigensystem

?RandomReal
?RandomComplex

Differential & Integral Calculus

Simple Indefinite/Definite Integrals

A Curious Quirk Regarding Mathematica's Use of the Word "Assumptions"

Functions Defined by Integrals

Numerical Integration

Ordinary & Partial Differentiation

Ordinary Derivatives: Functions of a Single Variable

Partial Derivatives: Functions of Several Variables

Derivatives of Unspecified Functions

Implicit Differentiation

Maxima & Minima

Limits & Series

?Limit
?Series

Evaluation of Limits

Construction and Summation of Power Series

Laboratory 4

Obtaining/Displaying Solutions of Ordinary Differential Equations

?DSolve
?NDSolve

Digression: Stan Wagopn's Extraction Trick

The Slope Field Concept

Needs["VectorFieldPlots`"]

?VectorFieldPlot

Harmonic Oscillator

Graphic of Particle on a Spring

Damped Harmonicv Oscillator

Underdamped Display with Adjustable Damping Coefficient

Phase Space Methods

Harmonically Forced Damped Oscillator

Simple Pendulum

Pendulum Graphic

Damped Pendulum

Animated Damped Pendulum Graphic

Ballistics

Planetary Motion

Initial Conditions Replaced by Endpoint Conditions

An Unexplored Resource: Equation Trekker

Laboratory 5

Partial Differential Equations

Waves on a String

Accommodating Prescribed Boundary Conditions: the Clamped String

Effect of Releasing a Clamp

Gaussian Pulse on a Clamped String

Solution by "Separation of Variables"

Vibration of a Circular Drumhead

?ArcTan

Curvilinear Coordinate Systems

To and From Various Coordinate Systems

Evaluating the Jacobian

Grad, Div, Curl & Laplacian

Total Derivatives, Total Differentials & Fractional Change

Logarithmic Differentiation

Laboratory 6

Recursive Processes

Background

Basic Tools

?Nest

Wagon's Cobweb Plot

Logistic Map: Bifurcation & the Onset of Chaos

Wagon's Bifurcation Plot

Comparison with Other Maps:  First Glimpse of Universality

Coupled Nonlinear ODEs with Chaotic Solutions

Rikitake;s Model of Geomagnetic Field Reversal

Lorenz Model

Fitting Curves to Data

Importing Data

Curve Fitting Techniques

?Interpolation
?Epilog
?Map
?Fit

Fourier Analytic Curve Fitting