Mathematica Course for Science and
Mathematics
Class: Winter 2006, PHYS 399---Undergraduate
Science/Mathematics
Instructor: Robert L Zimmerman
Office Hours:
By appointment
email: bob@zim.uoregon.edu
Mathematic Course Overview
Mathematica is a computer-based software system for doing
symbolic calculations, numerical analysis, and visualizing and plotting data.
The program has an array of functions and procedures that can be adapted to perform
calculations for almost any needs. It is useful to for doing mathematics,
physics, chemistry, biology, geology, engineering, and economics---anything
that requires symbolic or numerical analysis. The goal of this course is to introduce the reader to
Mathematica’s graphics, symbolic calculations, numerical calculations, and
programming. Although there are no
official prerequisites for the course, the typical student should have at least
1 year of calculus, some knowledge of linear algebra and differential
equations. Enrollment is limited to 18 students. The grade for the course will be based on class
attendance, assignments and projects.
The course will cover the following topics:
Notebooks
Part I Foundations
Mathematica
Lecture one: Fundamental Commands
Mathematica Lecture three: Simple Graphics
Mathematica
Lecture two: Fundamental
Calculations
Mathematica
Lecture four: Simple User-Defined
Functions & Procedures
Part II Advanced Procedures
Mathematica
Lecture five: Advanced
Procedures
Mathematica
Lecture six: Advanced
Two-dimensional Graphics
Mathematica Lecture seven: Advanced Three-Dimensional
Graphics
Mathematica
Lecture seven: Algebraic Equations
Mathematica
Lecture eight: Vectors, Tensors and Matrices
Mathematica
Lecture nine: Functions and Calculus
Mathematica Lecture ten: Expansions in Orthogonal Series
Mathematica Lecture eleven: Differential Equations
Part III Applications
Mathematica Lecture twelve: Displaying and Fitting Data
Mathematica Lecture thirteen: Statistical Applications
Mathematica Lecture fourteen: Chemistry Applications
Mathematica
Lecture fifteen: Physics Applications
Mathematica Lecture sixteen: Biology Applications
Mathematica Lecture seventeen: Mathematics Applications
All lectures and problems are available as Mathematica
notebooks.
Mathematica notebooks for
the Lectures and Assignments
Part I Foundations
1.
Fundamental Commands
Mathematica Notebook One
Assignments for Notebook one (Solutions Deleted):
Assignments
Assignments for Notebook one (Solutions Included):
Assignments
Contents
1. Getting Started
1. Notebook and Cells: Input and Output, Grouping Cells, Text Style, Standard and Traditional Forms
2. On-line Help: Using ?, Aborting
3. Messages: Warning Messages, Send an Email Message or open
a URL
Summary
2. Calculator Commands
1. Arithmetic Commands: Real Input, Complex Input, Sums and Products, Naming Results
2. Roots and Powers: Powers, Attributes
Summary
3. Common Built-in Functions
1. Logarithmic and Exponential Functions:
2. Trigonometric Functions: Trigonometric functions, Inverse Trigonometric Functions
3. Hyperbolic Functions:
4. User-Defined Functions
Summary
4. Lists and Tables
1. Random Numbers:
2. Range:
3. Table:
4. TableForm:
5. Numerical Expressions
1. Exact and Approximate Numbers: Exact and Approximate, Converting Exact to Approximate, Converting Approximate to Exact, Displaying Numbers
2. Numerical Commands: Finding the Type of Numbers, Number Commands
3. Constants: Built-In, Constants in Add-On Packages
6. Internal Representation of Commands
1. FullForm:
2. Changing Heads:
3. Attributes:
Summary
2.
Simple Graphics
Mathematica Notebook Two
Assignments for Notebook two (Solutions Deleted):
Assignments
Assignments for Notebook two (Solutions Included): Assignments
Contents
1. Plot and Plot3D
2. ParametricPlot
3. Graphic Primitives
Fundamental
Mathematica Notebook Three
Assignments for Notebook three (Solutions Deleted):
Assignments
Assignments for Notebook three (Solutions Included): Assignments
Contents
1.Expressions and Lists
1. Making Substitutions with Rules: Replacing terms once,
Repeated Substitutions, Delayed substitution, Application of rules to Lists
2. Parts of Expressions and Lists: Parts of Expressions,
Parts of Lists, Mapping Commands over Lists
Summary
2. Selecting Terms
1. Logical Commands and Q-Test: Logical Commands, Q-Tests
2. Selection and Cases: Using Select, Using Cases
3. Sort
Summary
3.
Simplifying Expressions
1. Simplifying Expressions
2. Trig Simplifications
3. Complex Simplification
Summary
4. Algebraic
Equations
1. Analytic
2. Numerical
Summary
5. Calculus
1. Integration:
2. Derivative:
3. Limits and Series:
4. Differential Equations:
Summary
Assignments for Notebook four (Solutions Included):
Assignments
Contents
1. User-Defined Functions
1. Making Functions: Delayed (:= ) and Immediate( =) Evaluations, Multiple Underscores, N-tuple Inputs, Multiple Definitions, Using both Immediate and Delayed Evaluations, Pure Functions, InPut Form: Prefix, Postfix and Infix, Attributes
2. Functions with Several Steps: Module and Block
3. Compiled Functions:
Summary
2. Functions and variables with tests and Patterns
1. Restricting Variables
2. Restricting the Head of a variable
3. Restrictions apply to the Function
3. Rules with Restrictions
4. Assigning Properties with f/:lhs=rhs
1. Assigning Properties to Functions f/:f[x_] f[y_]:=f[x+y]
2. Defining a Complex Symbol
3 Angular Momentum Operator
4. Declaring Variables
5. Advanced Procedures Mathematica Notebook Five
Assignments for Notebook five (Solutions Deleted): Assignments
Assignments for Notebook five (Solutions Included): Assignments
Contents
1. Do, While, For and With
1 Do
2. While
3. For
4. With
2. Branching Procedures If, Which, Switch
1. If
2. Which
3. Switch
3. Advanced Procedures
1. NestList and Nest:
2. FixedPoint and FixedPointList:
3. FoldList and Fold:
4. Inner and Outer
4. Style of Programing
6. Advanced Two-Dim
Graphics Mathematica Notebook Six
Assignments for Notebook six (Solutions Deleted):
Assignments
Assignments for Notebook six (Solutions Included):
Assignments
Contents
7. Advanced Three-Dim
Graphics Mathematica Notebook Seven
Assignments for Notebook seven (Solutions Deleted): Assignments
Assignments for Notebook seven (Solutions Included): Assignments
Contents
7. Algebraic
Equations Mathematica Notebook Seven
Assignments for Notebook seven (Solutions Deleted): Assignments
Assignments for Notebook seven (Solutions Included): Assignments
Contents
1.
Polynomial Equations
1.
Numerical Equations:
2.
Symbolic
3.
High-degree Polynomial Equations:
4.
Coupled Equations: Eliminating Variables, and Linear Solve
2. Non-Polynomial Equations:
1. Transcendental and Other Equations:
2. FindRoot:
3.
Equations with Logic Conditions
1.
Roots and Reduce:
2.
Equations with Logic operators:
4.
Constrained Equations
1.
Using Solve with Abs and Min:
2.
Conditional Solve with package:
3.
Maximum and Minium
4.
InequalitySolve
5.
Solving inequalities with Graphics:
5.
Recurrence Equations
1. RSolve:
8. Vectors, Tensors, and
Matrices
Mathematica Notebook Eight
Assignments for Notebook eight (Solutions Deleted): Assignments
Assignments for Notebook eight (Solutions Included): Assignments
Contents
1. Lists
1.
Replacing and Adding Elements
2.
Rearranging Elements
3.
Combining Lists
4.
SubLists
2.
Vectors
1.Vector Arithmetic
2.
Complex Vectors
3.
Base Vectors
3.
Matrices
1.
Making Matrices
2.
Arithmetic Commands
3.
Matrix-Vector Multiplication
4.
Matrix-Matrix Multiplication
5.
Matrix Powers
6.
Matrix Graphics
7.
Eigenvalues and Eigenvectors
8.
Pauli spin matrices
9. Functions and Calculus
Mathematica Notebook Nine
Assignments for Notebook nine (Solutions Deleted):
Assignments
Assignments for Notebook nine (Solutions Included):
Assignments
Contents
10. Expansions in
Orthogonal Series
Mathematica Notebook Ten
Assignments for
Notebook ten (Solutions Deleted):
Assignments
Assignments for Notebook ten (Solutions Included):
Assignments
Contents
11. Differential
Equations
Mathematica Notebook Eleven
Assignments for Notebook eleven (Solutions Deleted):
Assignments
Assignments for Notebook eleven (Solutions Included): Assignments
Contents
Part III Applications
12. Displaying and
Fitting Data Mathematica Notebook Twelve
Assignments for
Notebook twelve (Solutions Deleted):
Assignments
Assignments for Notebook twelve (Solutions Included): Assignments
Contents
13. Statistical
Applications
Mathematica Notebook Thirteen
Assignments for
Notebook thirteen (Solutions Deleted): Assignments
Assignments for Notebook thirteen (Solutions Included): Assignments
Contents
14. Chemistry
Applications
Mathematica Notebook Fourteen
Assignments for Notebook fourteen (Solutions Deleted):
Assignments
Assignments for Notebook fourteen (Solutions Included): Assignments
Contents
15. Physics Applications
Mathematica Notebook Fifteen
Assignments for Notebook fifteen (Solutions Deleted):
Assignments
Assignments for Notebook fifteen (Solutions Included): Assignments
Contents
16. Biology Applications
Mathematica Notebook Sixteen
Assignments for Notebook Sixteen (Solutions Deleted):
Assignments
Assignments for Notebook Sixteen (Solutions Included): Assignments
Contents
17. Mathematics
Applications
Mathematica _________
Assignments for Notebook Sixteen (Solutions Deleted):
Assignments
Assignments for Notebook Sixteen (Solutions Included): Assignments
Contents
