M427K Fall 2009


Unique #:     57720                     4961

Lecture:      TTh 12:30-2:00 in JGB 2.216
Discussion:   MW 1:00-2:00 PM in WRW 102
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 2:05-3:25 in RLM 12.130
TA:           James Maciejewski (jmaciejewski@math.utexas.edu)
TA Hours:     TWTh 11:00-12:00 and Thu 5:00--7:00 in RLM 12.120
Link to this file: www.ma.utexas.edu/users/kbi/COURSES/TERM/09F/427K/M427K.html

Grading Scheme
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. 6-8 homework projects count another 15%, and so do quizzes during discussion sessions. The comprehensive final test counts 25%. Absences drag down the grade as explained below. 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.
Here are some recent grade distributions resulting from this grading scheme.
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 Thursdays during class time:
October 1, October 29, and December 3. The final test is scheduled for Thursday, December 10, from 2:00PM to 5:00 in JGB 2.216. Put these dates on your calendar now, but check them regularly on this very page during the semester.
Quizzes: They will be given regularly during the discussion sessions.
Homework Projects: These will be assigned in due time and will be published at the bottom of this very page. They are mostly done on the computer using Maple or Mathematica or Matlab (MMM). Their purpose is to make sure that you have some computer literacy, develop some skill in writing a technical report, and to foster collaboration. They are to be done in groups of 3-4. Give me suggestions for a group of 2-4 students you would like to collaborate with; if you suggest a group of 2 or 3 students I will fill it from the class roster to make a group of 4. I will not instruct you how to log in, use MMM, etc; you are supposed to learn this (slowly) by discovering the help facilities of the programs (MMM). You may wish to make sure that at least one of the members of your group is slightly computer literate. Each project counts about 3%, but the total depends on how you are graded (Grades A-F) by your team members. If you get a D or F by all other members in your group, you lose the entire project grade, which is worth 15%. This is to discourage freeloaders.
Once in a while conflicts arise within a group, mostly when one of the members does not carry his/her weight. In this case you might try the UT Conflict Resolution Center at 232-1724. Resolving your conflict is their (free) mission.
Get an account on the Math computers by simply going to RLM 7.122 and requesting one. Have your UT-EID ready. Get help there for any project by asking the tutors, who are there during long hours (M-F 8:00AM - 9:00PM, Sat 9:00AM - 5:00PM, Sun 2:00PM - 5:00PM).
How to learn: The most efficient way to learn the material is to collaborate and to read ahead. I will post slides covering the next one or two lectures on the web. They can serve as your notes, so you won't have to scribble along. You should read them ahead of the lecture, so you can ask questions during the lecture.
Asking questions is your civic duty!
Make use of the Learning Skills 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.
Attendance: There are very good reasons to attend the classes you paid for. Also, I have collected some statistics in previous classes, and found that on the average 3 lectures missed or 6 lectures/discussions missed during the semester will lower the final grade by one letter grade. I'll elevate this from a statistic to a policy: I will check class attendance. The third, fourth, and any further absence will cost 3 points (3%) each.
``Absence'' means ``Absence for any reason'', death, visit to the doctor, sporting or cheerleading event, and hangover alike. So do not use your quota of absences frivolously and then plead hangover, sports, sickness, or death to extend your quota. It won't fly. This is not intended to be punitive, rather, to provide that extra little push our weak flesh needs from time to time. Students find a way to come to class most of the time, and this rule hardly ever needs to be applied. On the other hand, since I started to require attendance grades have gone up by nearly one letter grade on the average.
Curve: I do not grade on the curve. The scheme is: 90-100: A, 80-89.9: B, 70-79.9: C, 60-69.9: D, below 60: F.
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 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!
Thursday August 27: Introduction, Classification, FOLODE
Lecture 1. Practice: p 7 # 1, 3, 5, 11, 13, 15, 17, 19, 21; p 15 # 1-7; p 24 all.
Tuesday September 1: Separable FOODE .
Lecture 2. Practice: p 39 # 1-38; p 47 # 1-20.
Thursday September 3: Applications to Modelling
Lecture 3. Practice: p 59 # 1-14.
Tuesday September 8: Exact equations, integrating factors.
Lecture 4. Practice: p 99 # 1-22; 25-31.
Thursday September 10: Euler Approximation.
Lecture 5. Practice: p107 # 1-4.
Tuesday September 15: Second Order Linear ODE (SOLODE), Homogeneous Equations with Constant Coefficients (HCCSOLODE), Existence and Uniqueness, Differential Operators, Fundamental Systems of Solutions, the Wronskian.
Determinants; Lecture 6. Practice: p142 # 1-28; p151 # 1-14.
Thursday September 17: Reduction of Order, Repeated Roots, Complex Roots
Complex Numbers; Lecture 7. Practice: p164 # 1-25; p172 # 23-30, 1-14.
Tuesday September 22: , Non-Homogeneous Equations, Variation of Parameters, Undetermined Coefficients
Lecture 8. Practice: p190 # 1-21; p184 # 1-26.
Thursday September 24: Examples
Lecture 9.
Tuesday September 29: Review
Review.
Thursday October 1: Test 1
Tuesday October 6: Mechanical & Electrical Vibrations
Lecture 11. Practice: p202 # 1-12.
Thursday October 8: Review of Power Series
Lecture 12. Practice: p249 # 1-20, 21-28.
Tuesday October 13: Power Series Solutions I & II
Lecture 13. Practice: p259 # 1-14, 16-21; p265 # 1-17
Thursday October 15: Euler Equations
Lecture 14. Practice: p276 # 1-22.
Tuesday October 20: Regular Singular Points, Series Solutions there
Lecture 15. Practice: p282 # 1-16; p290 # 1-17.
Thursday October 22: The Laplace Transform
Lecture 16. Practice: p311 # 1-24; p320 # 1-16; p329 # 1-17.
Tuesday October 27: Review.
Thursday October 29: Test 2.
Tuesday November 3: Laplace Transform coninued: Step Functions, the Dirac Function, Convolution
Lecture 17. Practice: p337 # 1-16; p344 # 1-12, 17-22; p351 # 3-11, 13-18.
Thursday November 5: Laplace Transform coninued. Approximation.
Examples. Lecture 18. Practice: p451 1ab-12ab.
Tuesday November 10: The Heun and Runge-Kutta Methods.
Lecture 19. Practice: p458 1-12; p463 # 1-12.
Thursday November 12: PDE: Heat Conduction I
Lecture 20. Practice: p618 # 1-6; p593 # 1-24.
Tuesday November 17: Fourier Series & Gibbs' Phenomenon
Lecture 21. Practice: p608 # 1-6, 15ab-22ab; p600 # 1-11.
Thursday November 19: Heat Conduction II
Lecture 22. Practice: p620 # 1-8, 9-13.
Tuesday November 24: Wave Equation
Lecture 23. Pictures. Practice: p632 # 1-8.
Thursday November 26:Thanksgiving
Tuesday December 1: Review
Thursday December 3: Test 3
Thursday December 10, 2:00 PM: Final Test in TBA.

Click here for the Homework Projects.