SYLLABUS

MATH 13

ORDINARY DIFFERENTIAL EQUATIONS

WHAT, WHERE & WHEN

 

Ordinary Differential Equations, Math 13, will have a new registration code each time it is offered.  Its meeting times and places will vary from term to term.  Consult the current schedule of classes for this information.

 

TEXT

The text and use of software will be determined by the instructor.

 

TOPICS

The subjects to be covered in the course are roughly the following.

  • What is an Ordinary Differential Equation?

 

Fundamental Principle:  f ’=0 => f =constant

 

 

Linear Equations

 

 

Separable Equations

 

 

Exact Equations

 

 

Integrating Factors

 

Homogeneous Equations

 

Existence and Uniqueness Theorem

 

 

§2.11 example, and analytic conditions

 

  • Higher order linear equations

 

Constant Coefficients

 

Non-homogeneity

 

Undetermined Coefficients

 

Variations of Parameters

 

Series Solutions

 

Laplace Transforms

 

  • Systems of Equations

           

 

Eigenvalues and Eigenvectors

 

Matrix Methods, Diagonalization and Canonical Form

 

·        Numerical Methods

 

Runge-Kutta

 

Stability

 

GENERAL INFORMATION

The only known way to learn the subject is to do problems. A great deal of your time will be devoted to practice and discussion of problems, so there should be ample time to deal with difficulties arising in your studies. You should feel free to ask anyone for help, or work with your classmates, on assignments.  Reasonable behavior that will help you learn the subject is certainly acceptable.

In general it will be helpful to have several writing utensils, a calculator and scratch paper handy as you work on this material.  You will want to have a file, folder, or notebook in which you keep all of your notes.  Much of this can be kept on computers, and you should also have a file on a hard drive and some sort of memory storage device (ZIP disc, memory stick, or some such) on which you keep all of your class related material.

Any feedback you have regarding the course will be welcome and deeply appreciated. Please feel encouraged to comment (anonymously or otherwise, as you please). And certainly at all times feel free to ask questions regarding either the structure of the class or the material being covered.

 

ATTENDANCE

You are not required to show up for class.  Nevertheless, attendance will be recorded daily for administrative purposes. You are responsible for the work, and if you do not attend the responsibility to cover missed material is yours.

 

EXAM INFORMATION

A final exam will be given at a time set by the college.  Midterm arrangements will be made by the instructor.

 

HOMEWORK SUBMISSION

Homework arrangements will be made by the instructor.

 

GRADING

Grading arrangements will be made by the instructor.