Mathematica Course for Science and Mathematics


Class:   Winter 2006, PHYS 399---Undergraduate Science/Mathematics

Instructor:    Robert L Zimmerman

Office: 448 Willamette

Office    Hours:  By appointment

Phone: 6-5211



                                       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:



                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                                                                                                        


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

2. Calculator Commands

1. Arithmetic Commands: Real Input, Complex Input, Sums and Products, Naming Results

2. Roots and Powers: Powers, Attributes

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


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:


2.        Simple Graphics                             Mathematica   Notebook Two 

Assignments for Notebook two (Solutions Deleted):                       Assignments          

Assignments for Notebook two (Solutions Included):                       Assignments


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


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


2. Selecting Terms

1. Logical Commands and Q-Test: Logical Commands, Q-Tests

2. Selection and Cases: Using Select, Using Cases

3. Sort


 3. Simplifying Expressions

1. Simplifying Expressions

2. Trig Simplifications

3. Complex Simplification


4.  Algebraic Equations

1. Analytic

2.  Numerical


5. Calculus

1. Integration:

2. Derivative:

3. Limits and Series:

4. Differential Equations:



4. Simple User-Defined Functions and Procedures

                                                                                            Mathematica Notebook Four

Assignments for Notebook four (Solutions Deleted):                                 Assignments                              

Assignments for Notebook four (Solutions Included):                                Assignments           


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:


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


                               Part II Advanced Procedures



5. Advanced Procedures                              Mathematica      Notebook Five

Assignments for Notebook five (Solutions Deleted):                           Assignments                              

Assignments for Notebook five  (Solutions Included):                        Assignments              


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            



7. Advanced Three-Dim Graphics Mathematica  Notebook Seven    

Assignments for Notebook seven (Solutions Deleted):              Assignments                              

Assignments for Notebook seven  (Solutions Included):         Assignments                               



7. Algebraic Equations                  Mathematica  Notebook Seven    

Assignments for Notebook seven (Solutions Deleted):              Assignments                              

Assignments for Notebook seven  (Solutions Included):         Assignments                               


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                               


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                              


10. Expansions in Orthogonal Series           Mathematica  Notebook Ten       

Assignments for Notebook ten (Solutions Deleted):                        Assignments                              

Assignments for Notebook ten (Solutions Included):                 Assignments                               


11. Differential Equations                   Mathematica  Notebook Eleven    

Assignments for Notebook eleven (Solutions Deleted):               Assignments     

Assignments for Notebook eleven (Solutions Included):              Assignments   



                               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


13. Statistical Applications           Mathematica  Notebook Thirteen

 Assignments for Notebook thirteen (Solutions Deleted):            Assignments     

Assignments for Notebook thirteen  (Solutions Included):           Assignments


14. Chemistry Applications                  Mathematica  Notebook Fourteen   

Assignments for Notebook fourteen (Solutions Deleted):             Assignments     

Assignments for Notebook fourteen  (Solutions Included):           Assignments


15. Physics Applications                                  Mathematica  Notebook Fifteen    

Assignments for Notebook fifteen (Solutions Deleted):                    Assignments     

Assignments for Notebook fifteen (Solutions Included):                   Assignments


16. Biology Applications                             Mathematica  Notebook Sixteen

Assignments for Notebook Sixteen (Solutions Deleted):                  Assignments     

Assignments for Notebook Sixteen (Solutions Included):                Assignments


17. Mathematics Applications                   Mathematica  _________

Assignments for Notebook Sixteen (Solutions Deleted):                  Assignments     

Assignments for Notebook Sixteen (Solutions Included):                Assignments