Course TitleTopics in Linear Algebra and Differential Equations

Catalog Description: This course provides a modern introduction to ordinary differential equations. We will emphasize analytic, geometric and numerical approaches to solving differential equations. We will also consider how differential equations can be used as powerful tools in modeling real world phenomena.

There will be a focus on linear differential equations. The tools of linear algebra will be extensively used to study such equations. After discussing first order equations and systems of first order equations, we will see how higher order equations can be analyzed.

We will then turn our attention to nonlinear differential equations, with a focus on autonomous systems and questions of stability. This unit will conclude with an examination of the exciting new area of chaos theory.

We will finish the course with an examination of some numerical methods to approximate the solutions of differential equations.

Instructor :Michael Olinick molinick@middlebury.edu, 314 Warner, phone 443-5559. Home telephone: 388-4290. Office Hours: Monday, Wednesday, and Friday from 9 to 10 a.m. And Noon to 1 p.m.; Tuesday from 9:30 to noon. I am always happy to make an appointment to see you at other mutually convenient times.

Meeting Times: MA 300A: MWF 10:10-11:00., Warner 202

                                    MA 300B: MWF 11:15 - 12:05, Warner 202
 
 

Computer Algebra System: The development of powerful computer algebra systems for personal computers has revolutionized how students can investigate the behavior of many topics in mathematics, especially differential equations. We will emphasize the use of Maple, but you can also employ Mathematica or other software.

Prerequisites: MA 200 (Linear Algebra)

Textbooks: William E. Boyce and Richard C. DiPrima, Elementary Differential Equations and Boundary Value Problems (Interactive Learning Version), Seventh Edition, Wiley: 2001. This version of the text comes with a CD which contains the entire contents of the book, ODE Architect software, a 41 page guidebook to the software, links to the text’s homepage, and other helpful features.

Kevin R. Coombes, Brian R. Hunt, Ronald L. Lipsman, John E. Osborn and Garrett J. Stuck, Differential Equations with Maple™, Second Edition, Wiley: 1997.

Your daily assignments will include a few pages of reading in the texts. Be certain to read the book carefully (with pencil and paper, or occasionally Maple, close by!) Complete the relevant reading before coming to class and before tackling the Warm Up Exercises or Problem Sets.

Requirements: There will be two midterm examinations and a final examination in addition to required homework assignments. The midterm examinations will be given in the evening to eliminate time pressure. Tentative dates for these tests are:

The College's Scheduling Officer has tentatively set Saturday, May 18 from 9 a.m. to Noon as the time and date of the final exam.
 
 

Homework: Mathematics is not a spectator sport! You must be a participant. The only effective way to learn mathematics is to do mathematics. We occasionally assign some challenging problems which everyone may not be able to solve. You should, however, make an honest attempt at every problem.

You may use your notes, textbooks, calculators, and any computer software you have available (including Maple ) to assist with the homework. Bear in mind, however, that none of these will be permitted during examinations.

I encourage you to talk to each other about the Warm Up Exercises and Problem Sets. The final write up must be done alone. You should not have access to a colleague’s assignment while writing up your own. Warning: The College deals quite severely with cases of plagiarism, cheating, or other forms of academic dishonesty.

Homework must be done neatly and legibly. Shoddy work will not be accepted for grading. Staple your assignments! There will not be a great deal of partial credit given for obviously incorrect answers. You should check your results where possible or at least examine them to see whether they are plausible.

Because I will distribute solution sheets to assigned work on the day it is due, late papers can not be accepted. Start each assignment early and work on them every day. You will probably not be able to complete a Problem Set if you wait to begin until the night before it is due.
 
 

Important Thought:One of the essential characteristics of college life that distinguishes it from secondary school is the increased responsibility placed on you for your own education. Most of what you will learn will not be told to you by a teacher inside a classroom. Even if our model of you were an empty vessel waiting passively to be filled with information and wisdom, there wouldn’t be time enough in our daily meetings to present and explain it all. We see you, more appropriately, as an active learner ready to confront aggressively the often times subtle and difficult ideas our courses contain. You will need to listen and to read carefully, to master concepts by wrestling with numerous examples and problems, and to ask thoughtful questions.
 
 

Grades: Grades in the course will be based on the two midterm examinations, Warm Up Exercises, Problem Sets, and the comprehensive final exam. The relative weights oft he various components of the course are roughly as follows:

Help: Please see me immediately if you have any difficulties with this course. Do not hesitate to utilize office hours. I welcome questions of any sort, including questions on assignments not yet handed in. In additions, I always appreciate your opinions and comments concerning the course.

A Final Word: There is a lot of exciting mathematical material in this course. Have fun with it!