Course content: Introduction to first order differential equations, linear differential equations with constant coefficients, and systems of differential equations; vector spaces, linear transformations, matrices, determinants, linear dependence, bases, systems of equations, eigenvalues, eigenvectors, and Laplace transforms.

The required text for this section of 2090 will be Differential Equations and Linear Algebra, second edition, by Stephen W. Goode, published by Prentice-Hall, Inc., 2000. In terms of the textbook, the course content will be selected material from Chapters 1 through 9.

A more detailed program, with assignments and lecture summaries, will be developed as the semester proceeds at http://www.math.lsu.edu/~mcgehee/2090/guide.html.

The prerequisite for 2090 is 1552 (Calculus II). Because of the overlap in material covered, there are restrictions on coursecredit, as follows: Credit will be given for only one of 2065, 2070, and 2090. Credit will be given for only one of 2085 and 2090.

Requirements: There will be three one-hour tests, a two-hour comprehensive final exam, and exercises to write up.

The classroom is equipped with a computer and projector, and during lectures we will sometimes look at graphics and other output generated by Mathematica. You may find it helpful to work with Mathematica or other such software, available in many computer labs on campus. The tests will sometimes require you to interpret and apply given computer output. On most or all of the tests, however, the use of cell phones, calculators, and computers may be prohibited.

Please look at the schedule of hour tests and tell me as soon as possible if you have any problem with any of the dates. They are subject to change, but for the sake of fairness I will want to make changes only with ample notice, after we discuss it in class.

I will assign selected exercises to be written up and turned in, with definite deadlines. The grade on an assigned exercise will follow a numerical scale, thus: 9 or 10, A; 7 or 8, B; 5 or 6, C; 3 or 4, D. At the bottom is a statement of the scoring criteria.

Your written solutions to exercises should be easy to read, neat, organized, clear, and well-written - as well as correct. Your work must be your own, with the following exceptions: You may consult the text and other books. You may consult me for help. To a limited and reasonable extent, you may consult other persons, or work with others in the class.

I may sometimes make copies of your solutions to exercises and test questions and distribute them to the class, with attribution.

In addition, I will frequently suggest other problems for you to do on your own (not to be turned in), as a further guide for study.

Grading Formula: Let T denote your average grade on the hour tests; P , your overall grade on exercises; and E , your grade on the final exam. Let X be the higher of T and E , except that X may be raised if you have done more than 15 exercises. Your overall grade in the course will be no lower than
 

The grade P: You will get points and credit only for problems on which your grade is 7 or better. You are expected to earn credit for at least 30 problems; if PT is your total number of points, and you have credit for Q problems, then

The grade X: Your grade X may be higher than max(T,E) if during the semester you get credit for more than 30 problems.  In fact, if you do an outstanding job on the problems, your overall score on the problems can count up to 40% of your course grade.  Here is how X will be computed. Assuming that Q is at least 30 but no more than 60, then

I expect you to attend class faithfully and to keep up with assigned work. When you are absent, or if you are late to class, or if you leave class early, I will assume that you have good reason; but please let me know why. If you have difficulties of any kind that affect your work, I will be glad for you to tell me about them. Whenever there is some way you think I can help, please ask.

It will be best for you not to miss scheduled tests; but if you find that you are unable to take a test (or even the final exam) at the appointed time due to illness or other difficulty, please discuss it with me as soon as possible; there will be deadlines for taking make-ups. Once you have taken the final, or any other test, a re-take is not allowed. When a test or problem set is graded and handed back to you, you should look it over carefully, and if you have any question or complaint about the grading, you should discuss it with me. It never hurts to ask.

Your background will have an important effect on how well you do in the course. It is important to have good notes from your calculus courses, and/or to be comfortable with using your calculus textbook for review and reference. It is normal, during a mathematics course, to review, re-learn, or learn background material. It is OK to ask for help with it. But it is your responsibility.

To benefit from the lectures, you should be up-to-date with your reading and other assignments when you come to class. If you can follow the lectures and get what's going on during class, great. If not, take notes and work through them before the next class period. I welcome students' asking questions and catching my mistakes during class.

Read the book. Do not expect to read a math book fast. Read the book actively. Try to be convinced that you understand each line before going on to the next. After reading a worked example, close the book and try to write out a complete solution. An assignment to "read Section x" includes not just a thorough reading but also doing a few of the exercises at the end.

When you do problems: Study systematically the related lectures and book sections first. When you work a problem, try to arrive at a solution that you have confidence in before looking at the answer in the back of the book.

Finally, some personal advice: Students in Math 2090 often have a difficult schedule. Have due respect for what you're up against. Take care of your health and of your general well-being. You need to be in good physical condition to succeed (and to stay awake in class). Get the physical exercise that you need, and eat properly. Do what you need to do to assure that you have helpful conditions in the places where you live, work, and sleep. If you have emotional problems, get help, or at least find a friend to talk to; don't go it alone, and don't despair.
 
 

10.00 The Exercise is done completely. All answers are correct. Procedures and reasoning are made clear, though not in excessive detail, and are correct. All statements are correct. The paper is neat and readable. The writer uses complete sentences. (Remember that sentences can be written in mathematical symbols.) The writer uses symbols correctly, including the equal sign = and the symbol that means "implies," =>. The writer provides a sketch whenever one is asked for or needed to make things clear. Sketches are reasonably accurate and appropriately labeled.

8.00 or 9.00 The writer demonstrates a good understanding of the Exercise, although the criteria for a 10.00 are not all met. If there is an error in an answer, it is one that is not easily spotted; that is, it does not render the answer implausible. If there is an error in an answer, then it does not indicate a lack of understanding. It seems likely that if the writer attempted another similar Exercise, he or she would get it entirely correct.

6.00 or 7.00 The writer has correctly done most of the Exercise. Or the writer followed a good procedure but made an error in carrying it out that he or she should have caught. The writer probably needs a bit of help before he or she can be expected to do another such Exercise correctly.