M427K Spring 2012


Unique #:     55650                   6655

Lecture :     TTh 2:00-3:30 in UTC 3.124
Discussion:   MW 3:00-4:00 PM in PHR 2.108
Textbook:     Boyce-DiPrima, "Elementary Differential Equations
              and Boundary Value Problems," nineth edition
Syllabus:     I,II,III,IV,V,VI,VIII,X with some deletions
Office Hours: TTH 3:30-5:00 PM in RLM 12.130
TA:           Tian Ding, tding@math.utexas.edu
TA Hours:     MW 4:00 - 6:00 PM in RLM 11.146
Link to this file: www.ma.utexas.edu/users/kbi/COURSES/TERM/12S/427K/427K.html

Grading Scheme
During most every lecture we'll have one or more short multiple-choice quizlets, which together will count 10% towards the course grade. They cover topics from the current and previous lectures. For these quizlets you will need to own and register an iClicker and to enroll in this course. If something goes awry with this process, bring your iClicker to the ITS office in FAC to have the ID read; write it down. It will be used to register your iClicker in Quest. (See the bottom of http://web4.cns.utexas.edu/quest/support/clicker/#register.) Read about Quest here.
There will be three (3) midterm tests, each worth 15% and covering the material presented prior to the test. The tests thus contribute 45% to the grade. The homework for the current week is collected in the discussion session on the Wednesday following the current week, and counts 10% towards the final grade. 6-8 homework quizzes count another 10%. The comprehensive final test counts 25%. Cheating is costly.
Tests: The worst (or missed) midterm test is replaced by the score from the final test if that improves the total. I can't allow you to miss two or more of the midterm tests, though, and there will be NO (0) make-up test. There are usually 5-6 problems per test, one of them an essay question, the other 4-5 from the assigned homework. I shall assign particularly useful homework problems from the book and pick all but one test problem from among them or from examples I worked out in class, perhaps slightly altered; this homework is not collected. Whoever does the assigned problems can hardly fail to pass with flying colors. The midterm tests are scheduled on the following days during class time:
February 16, March 29, and May 3. The final test is scheduled for Saturday May 12 at 2:00 PM in TBA. Put these dates on your calendar now, but check them regularly on this very page during the semester.
Homework and Homework Quizzes: Of the homework problems assigned for a lecture a very few are listed in boldface. These will be collected on the Wednesday of the following week. They count 10% towards the final grade.
Roughly every second week the TA will have a quiz during part of the discussion session in which one or two of the list of all problems are given verbatim. There will thus be 6-8 of these quizzes, and they count 10% towards the course grade. I encourage you strongly to work the homework problems in groups. Talking to your friends about these problems saves time and settles the math in the brain. By all means submit only one page of solutions per group and list on it the names of the collaborators.
How to learn: The most efficient way to learn the material is to collaborate and to read ahead. Make use of the Sanger Learning and Career Center! Also, the University of Texas at Austin provides upon request appropriate accommodations for qualified students with disabilities; for more information contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.
Peoples' brains are structured differently; some learn conceptually (about 40%), some by example after example (about 60%). For the latter there are the examples I'll develop during the lectures plus two hours (Mon & Wed) of recitation given over only to examples. Attend these recitation sessions and do the homework and you will get your fill of examples; don't expect me to do nothing but examples, I have to take care of the other 40% as well.
Curve: I do not like to grade on the curve; I like the scheme 90-100: A, 80-89.9: B, 70-79.9: C, 60-69.9: D, below 60: F. Students, however, seem to like being graded on the curve, so I shall deviate a little from the scheme above by assigning A-, B-, C- etc. to totals that don't quite make the cutoff for A, B, C, respectively.
I am not permitted to change this grading scheme, for example by assigning extra work if a few points are missing for a higher grade. Also, I do not cook the books, not even for the most charming, needy, or pushy student. So aim for a few points above what you actually need for your desired grade.
Regrades and Disputes: I grade very leniently. If I make a mistake in grading please let me know and I'll fix it--provided the request to change a score is made within one week of the test or homework in dispute being returned to the class. However, the way I apportion partial credit is my prerogative and I will not change it. I will not entertain arguments about it; they merely generate ill will.
Just in case disputes over your record should arise keep all tests, homeworks, quizzes etc.
The Goal
The syllabus for this course is big, even overcrowded. Nevertheless, we must cover it, since the results are needed for subsequent mathematics, physics, and engineering classes. The idea to go slowly and cover thoroughly only part of the syllabus is attractive but fails in the long run.
Here is what a student must know and be able to do in order to get an A:
I) He or she must be able to write simple paragraphs in answer to questions like these:
What does it mean that a function solves a differential equation? State the existence and uniqueness theorem(s). What classes of first order ordinary differential equations can you attack with special tools - what are these tools? What is the Wronskian, where in ODE does it appear, what does it do for you? Explain the method of reduction of order, of variation of parameters; where do they apply? Explain the method of undetermined coefficients; where does it apply? Explain power series and power series solutions; where do they converge? Same for regular singular points. Explain the Laplace transform and its application in ODE. What numerical methods are there (do you know), how do they compare in accuracy, efficiency, and computing time consumed? Describe the method of separation of variables in PDE's. What is a Fourier series; where does it converge, in which sense does it represent the function, how does it help in PDE's? Describe the Gibbs phenomenon. Etc. Describe separation of variables in PDEs.
II) Besides being able to show his/her understanding of the material as above, the A-student is able to do calculations as in the problems at the end of the sections in the book, including word problems: set up the corresponding differential equation, solve it, and interpret the result.
Here is a Practice Test in pdf format.
Here is a Practice Final in dvi format, in postscript format, in pdf format.
Here is a plan of the course. A course is a living and unpredictable thing.
Therefore this plan is highly preliminary and will change as the course develops!
Tuesday January 17: [QL] Introduction, Classification, FOLODE.
   Lecture 1. Homework, Due 01/25: Section 1.1 # 1, 2, 3, 5, 11, 13, 15, 17, 19, 21; Section 1.2 # 1, 2b, 3-7; Section 1.3 # 1, 2, 3, 4, 5-10, 11, 12, 13-28.
Thursday January 19: [QL] Separable FOODE.
   Lecture 2. Homework, Due 01/25: Section 2.1 # 1-4, 5, 6, 7-33; Section 2.2 # 1, 2, 3, 4, 5-9, 10, 11, 12, 13-21.
   Tuesday January 24: [QL] Applications to Modelling.
   Lecture 3. Homework, Due 02/01: Section 2.3 # 1, 2-6, 7, 8-12, 13, 14; Section 2.5 # 1, 2, 3-6.
Thursday January 26: UTC dark - No class
Tuesday January 31: [QL] Population dynamics; Exact equations, integrating factors.
   Lecture 4. Homework, Due 02/08: Section 2.6 # 1-2, 3, 4-18, 19, 20-22; 25-28, 29, 30-31.
Thursday February 2: [QL] Integrating factors, Euler Approximation.
   Lecture 5. Homework, Due 02/08: Section 2.7 # 1, 2-4.
Tuesday February 7: [QL] Second Order Linear ODE (SOLODE); HCCSOLODE, Complex Numbers, Complex roots; Existence and Uniqueness, Differential Operators.
   Lecture 6. Homework, Due 02/15: Section 3.1 # 1-3, 4, 5-9, 10, 11-28; Section 3.3 # 1-18, 19, 20-25.
Thursday February 9: [QL] Second Order Linear ODE (SOLODE): Fundamental Systems of Solutions, the Wronskian, Determinants, Abel's Theorem; Reduction of Order, Repeated Roots.
   Lecture 7. Homework, Due 02/15: Section 3.2 # 1-3, 4, 5-7, 8, 9-14.
Tuesday February 14: [QL] Review.
Thursday February 16: Test 1.
   Tuesday February 21: [QL] Non-Homogeneous Equations, Variation of Parameters, Undetermined Coefficients
   Lecture 9. Here are Several Examples. Homework, Due 02/29: Section 3.6 # 1-3, 4, 5-21; Section 3.5 # 1-11, 12, 13-26.
Thursday February 23: [QL] Mechanical & Electrical Vibrations.
   Lecture 10. Homework, Due 02/29: Section 3.7 # 1-5, 6, 7, 8-12.
Tuesday February 28: [QL] Review of Power Series.
   Lecture 11. Homework, Due 03/07: Section 5.1 # 1-3, 4, 5, 6, 7-22, 23, 24-28.
Thursday March 1: [QL] Power Series Solutions I & II.
   Lecture 12. Homework, Due 03/07: Section 5.2 # 1-4, 5, 6-14, 15, 16-21; Section 5.3 # 1-2, 3, 4-17
Tuesday March 6: [QL] Euler Equations.
   Lecture 13. Homework, Due 03/21: Section 5.4 # 1, 2, 3-14, 15, 16-19, 20, 21-22.
Thursday March 8: [QL] Regular Singular Points, Series Solutions There.
   Lecture 14. Homework, Due 03/21: Section 5.5 # 1-2, 3, 4, 5-12; Section 5.6 # 13-14, 15, 16-17.
Tuesday March 13: Spring Break
   Thursday March 15: Spring Break
   Tuesday March 20: [QL] The Laplace Transform I.
   Lecture 15. Homework, Due 03/28: Section 6.1 # 6-8, 9, 10-15, 16, 17-20; Section 6.2 # 1, 2, 3-13, 14, 15, 16, 17-20.
Thursday March 22: [QL] Laplace Transform II: Step Functions, the Dirac Function, Convolution.
   Lecture 16. Homework, Due 03/28: Section 6.3 # 1-2, 3, 4-9, 10, 11-19, 20; Section 6.4 # 1, 2-16; Section 6.5 # 1, 2, 3-12, 17-22; Section 6.6 # 3-5, 6, 7-11, 13-18.
Tuesday March 27: [QL] Review.
   Thursday March 29: Test 2.
   Tuesday April 3: [QL] Approximation.
   Examples. Lecture 17. Homework, Due 04/11: Section 8.1 # 1ab, 2ab-6ab,7ab,8ab-12ab.
Thursday April 5: [QL] The Heun and Runge-Kutta Methods.
   Lecture 18. Homework, Due 04/11: Section 8.2 # 1, 2, 3-12; Section 8.3 # 1, 2, 3-12.
Tuesday April 10: [QL] Heat Conduction I.
   Lecture 19. Homework, Due 04/18: Section 10.5 # 1, 2, 3-6; Section 10.2 # 1-15, 16, 17-18, 19, 20-24.
Thursday April 12: [QL] Fourier Series & Gibbs' Phenomenon.
   Lecture 20. Homework, Due 04/18: Section 10.4 # 1-2, 3, 4, 5-6, 15ab-22ab; Section 10.3 # 1, 2, 3-11.
Tuesday April 17: [QL] Heat Conduction II.
   Lecture 21. Homework, Due 04/25: Section 10.5 # 7-8, 9-13; Section 10.6 # 1-17.
Thursday April 19: [QL] The Wave Equation.
   Lecture 22. Pictures. Homework, Due 04/25: Section 10.7 # 1, 2-8.
Tuesday April 24: [QL] The Laplace Equation.
   Lecture 23. Practice: Section 10.8 # 1-3.
Thursday April 26: [QL] Review.
   Tuesday May 1: [QL] Review
   Thursday May 3: Test 3
   Saturday May 12: 2:00 PM Final Test in WEL 3.502.

Click here for the Past Quizzes.