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Math 2403, Spring 2008, Diffeqs

Please open the following document to get schedule of tests, coverage, and general course information such as grading policy:
CourseScheduleM2403Spring2008.pdf

FINAL EXAM is 8AM Thurs of exam week, in same room as our lectures (Physics L1). It covers through section 7.2. We did some problems from that section today (Tues) in class.
You may bring 25 cheat sheets (the 20 you made for past tests, plus 5 more for new material).
NOTE!! BE SURE TO BRING YOUR TABLE OF LAPLACE TRANSFORMS sheet.

We are now working on Ch 7, non-linear systems. The homeworks below now go through chapter 7 section 2.


Here are the 4 tests we had this semester:
Test1 M2403 spring08.pdf
Test 1 solutions
Test2 M2403 spring08.pdf
Test 2 solutions
Test3 M2403 spring08.pdf
Test 3 solutions
Test4 M2403 spring08.pdf
Test 4 solutions

Navraj Singh is holding a review session tonight (Tues, Apr 15) in Siles 268 at NOTE CHANGE: I THINK IT IS 7:30 INSTEAD of 5:30, and has kindly agreed to allow students from other sessions to attend if needed.

Test 4 (on Wed Apr 16)will cover sections 5.7, 5.8, first part of 5.9 (not anything about Routh criterion for stability, just look at the two homework problems for that section); and chapter 6 sections 1 through 5. We will cover section 6.6 but will not be on test 4, will carry forward perhaps to final.
The homeworks for the material starting in 5.7 and through chapter 6 (and some of ch 7 yet to be assigned) will not be collected because of time constraints, but of course you must do them to prepare for the tests and final exam.

Homework 3 (which will cover sections 4.6 through 5.6, just like the test) will be collected Monday, April 7.



TEST 3 has been postponed until Monday, March 31, as has been announced in class (twice). The test will cover from where the last test left off (in other words starting from section 4.6), through section 5.6. Right now in class we have gone over section 5.5 rather thoroughly, and will do section 5.6 on Thursday.
For test 3 you may have 5 cheat sheets, and in addition may have another page for table 5.3.1, the transforms page in your book. YOU MUST MAKE AND BRING YOUR OWN PAGE OF LAPLACE TRANSFORMS, they will not be distributed.


NOTE!! For test 2 you may have 5 cheat sheets (front and back, making 10 sides) and a calculator, just like last time.
NOTE!! Test 2 has been postponed 2 days, will now be on Wed, Feb 27. It will cover chapter 3 and chapter 4 through section 4.5.
Homework two, covering the same sections, will be collected on Monday, March 4.
note: You may look at the Fall 2004 diffeq class, test2ans.pdf prob. number 2, test3_ans.pdf problem number 2, oldquiz2s.pdf, spring-mass problems with no forcing function, oldquiz3s.pdf, numbers 2ad,4,6,9,11, which have a little overlap with what we covered in our text for this test. But most of the material we covered in ch 3 and ch. 4 does not appear on these, SO YOU SHOULD LOOK AT YOUR HOMEWORK PROBLEMS as the main source, always a good policy.

Here are some very elementary introductory notes about complex numbers; many of you said you had never studied them at all, and this is a beginning treatment I wrote up for a beginning calculus class. It shows the geometry of complex numbers, what multiplication and roots mean,etc. I may add another page if you want, to include the Euler's formula and exponential of a complex number, which is needed for our class.
Complex1.pdf
complex2.pdf
Complex3.pdf

NOTE!! Test 1, on Wednesday January 30, will cover through Chapter 2. The exam will be closed book, but you may make 5 pages of notes ("cheat sheets"), front and back of standard paper, that should be plenty. Calculators are allowed, but you must show all your work to get credit so you have to know how to do the calculus. The questions are not multiple choice, you write out your work.

NOTE: you can look back at the diffeq class from fall 2004 to see test1 and old quiz 1's from that class. A different book was used, but many of the questions overlap our coverage so it might help.

The homework up through chapter 2 will be collected on Monday, Feb 4, and spot-checked. Please turn it in in a way that is easy for your TA to handle, not just dog-eared together (unless your TA wants that!) and also make sure your name is legibly printed, first and last name so it is easy to identify with the class roll.

The following homework file will be updated (at the moment it has assignments through section 2 of Chapter 7, as of Apr 20):
Homework M2403Spring2008.pdf

Here are a couple of matlab m-files that illustrate Euler's method for numerically solving first order ode. The first one (my_euler.m) is a function that is called by the second one (euler_example.m), which sets the initial conditions, calls my_euler, and then plots the result. These are not very good programs; I haven't been able to gain access to a computer with matlab for more than a few minutes, so this is just something to get you started if you don't already know how to use matlab. Rather than using the script euler_example.m to call my_euler, you could just type in the initial conditions in your workspace (copying the ones in euler_example.m) and then type in the call to my_euler function which returns the array of y values and the array of t values that you can then examine in the workspace, and plot. So if you put my_euler.m in the place that your workspace looks for m-files (I forget what that is called), you can just call my_euler any time you want from your workspace.
my_euler.m has the actual f(t,y) hard-coded into it, for some particular diffeq, which you would have to modify each time you changed the diffeq. Better would be to have my_euler call some function my_funct.m or something, and then you would not have to modify my_euler for each new problem, only my_funct.m.
To use matlab effectively, you need to learn how to step through a function with the debugger which shows what happens at each step so you can see how it works (and catch where it goes wrong when you write an incorrect program). You'll have to browse around the workspace to figure out how to set a breakpoint in the function you want to step through, and then run the debugger which will stop wherever you put the breakpoint, and then you can step through the function one step at a time and observe the values that are calculated, etc.
If you call my_euler with some initial conditions and then plot the solution (that is, plot t versus y), you can then run my_euler again with different initial conditions and plot that solution curve while leaving the first one up. I forget the exact syntax - something like "hold" when you do the first plot so it will stay there? I will look that up when I get access to matlab again.
So if you are a beginner, go mess around with this and see what you can get to work until I get some better instructions for you. If you already know matlab, I'm sure you could do a better job than what I am telling you. Hopefully by Thursday I will have a better discussion to put up.

my euler.m
euler example.m