M427K Fall 2014


Unique #:     55605
Lecture :     TTh 12:30-2:00 in CPE 2.208 
Discussion:   MW 5:00-6:00 PM in PAI 2.48
Textbook:     Boyce-DiPrima, "Elementary Differential Equations
              and Boundary Value Problems," nineth edition
Syllabus:     I,II,III,IV,V,VI,VIII,X with some deletions
Instructor:   Klaus Bichteler, kbi@math.utexas.edu
Office Hours: TTH 2:05-3:25 in RLM 12.130
TA:           Matthew Pancia, mpancia@gmail.com
TA Hours:     MW 3:45-4:45 in RLM 10.126
Link to this file: www.ma.utexas.edu/users/kbi/COURSES/TERM/14F/427K/427K.html

Grading Scheme
During most every lecture we'll have one or more short multiple-choice quizlets, which will count 15% 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.) 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 quizzes count another 15%. 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 Thursdays during class time: October 2, October 30, and December 4. The final test is scheduled for Tuesday December 16 at 9:00 AM in WEL 2.122. Put these dates on your calendar now, but check them regularly on this very page during the semester.

Homework Quizzes: Of the homework problems assigned for a lecture a very few are listed in boldface. Roughly every second week we will have a quiz in which two of these problems are given verbatim, with possibly a small change (to discourage those who think the quizzes are exercises in the memorization of answers). There will thus be 6-8 of these quizzes, and they count 15% 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.
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 or go here.
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. However, I'll deviate a little from that 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 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!


Thursday August 28: [QL] Introduction, Classification, FOLODE.
   Lecture 1. Homework: Section 1.1 # 1, 2, 3, 5, 11, 13, 15, 17, 19, 21; Section 1.2 # 1, 2, 3-7; Section 1.3 # 1, 2, 3, 4, 5-10, 11, 12, 13-28.
Tuesday September 02: [QL] Separable FOODE.
   Lecture 2. Homework: Section 2.1 # 1-4, 5, 6, 7-33; Section 2.2 # 1, 2, 3, 4, 5-9, 10, 11, 12, 13-21.
Thursday September 04: [QL] Applications to Modelling.
   Lecture 3. Homework: Section 2.3 # 1, 2-6, 7, 8-12, 13, 14; Section 2.5 # 1, 2, 3-6.
Tuesday September 09: [QL] Exact equations, integrating factors.
   Lecture 4. Homework: Section 2.6 # 1-2, 3, 4-18, 19, 20-22; 25-28, 29, 30-31.
Thursday September 11: [QL] Integrating factors, Euler Approximation.
   Lecture 5. Homework: Section 2.7 # 1, 2-4.
Tuesday September 16: [QL] Second Order Linear ODE (SOLODE), Homogeneous Equations with Constant Coefficients (HCCSOLODE), Existence and Uniqueness, Differential Operators. Determinants.
   Lecture 6. Homework: Section 3.1 # 1-3, 4, 5-9, 10, 11-28.
Thursday September 18: [QL] Second Order Linear ODE (SOLODE): Fundamental Systems of Solutions, the Wronskian.
   Lecture 7. Read this for fun.
   Homework: Section 3.2 # 1-3, 4, 5-7, 8, 9-14.
Tuesday September 23: [QL] Reduction of Order, Repeated Roots, Complex Roots, Complex Numbers;
   Lecture 8. Homework: Section 3.3 # 1-18, 19, 20-25; Section 3.4 # 23-26, 27, 28-30, 1-8, 9, 10, 11-14.
Thursday September 25: [QL] Non-Homogeneous Equations, Variation of Parameters
   Lecture 9. Here are Several Examples. Homework: Section 3.6 # 1-3, 4, 5-21; Section 3.5 # 1-11, 12, 13-26.
Tuesday September 30: [QL] Buffer - Review.
Thursday October 02: Test 1.

Tuesday October 7: [QL] Undetermined Coefficients, Mechanical & Electrical Vibrations.
   Lecture 10. Homework: Section 3.7 # 1-5, 6, 7, 8-12.
Thursday October 09: [QL] Review of Power Series.
   Lecture 11. Homework: Section 5.1 # 1-3, 4, 5, 6, 7-22, 23, 24-28.
Tuesday October 14: [QL] Power Series Solutions I & II.
   Lecture 12. Homework: Section 5.2 # 1-4, 5, 6-14, 15, 16-21; Section 5.3 # 1-2, 3, 4-17
Thursday October 16: [QL] Euler Equations.
   Lecture 13. Homework: Section 5.4 # 1, 2, 3-14, 15, 16-19, 20, 21-22.
Tuesday October 21: [QL] Regular Singular Points, Series Solutions There.
   Lecture 14. Homework: Section 5.5 # 1-2, 3, 4, 5-12; Section 5.6 # 13-14, 15, 16-17.
Thursday October 23: [QL] The Laplace Transform I.
   Lecture 15. Homework: Section 6.1 # 6-8, 9, 10-15, 16, 17-20; Section 6.2 # 1, 2, 3-13, 14, 15, 16, 17-20.
Tuesday October 28: [QL] Buffer - Review.
Thursday October 30: Test 2.

Tuesday November 04: [QL] Laplace Transform II: Step Functions, the Dirac Function, Convolution.
   Lecture 16. Homework: 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.
Thursday November 6: [QL] Laplace Transform continued; Approximation.
   Examples. Lecture 17. Homework: Section 8.1 # 1ab, 2ab-12ab.
Tuesday November 11: [QL] The Heun and Runge-Kutta Methods.
   Lecture 18. Homework: Section 8.2 1-12; Section 8.3 # 1-12.
Thursday November 13: [QL] Heat Conduction I.
   Lecture 19. Homework: Section 10.5 # 1, 2, 3-6; Section 10.2 # 1-15, 16, 17-18, 19, 20-24.
Tuesday November 18: [QL] Fourier Series & Gibbs' Phenomenon.
   Lecture 20. Homework: Section 10.4 # 1-2, 3, 4, 5-6, 15ab-22ab; Section 10.3 # 1, 2, 3-11.
Thursday November 20: [QL] Heat Conduction II.
   Lecture 21. Homework: Section 10.5 # 7-8, 9-13; Section 10.6 # 1-17.
Tuesday November 25: [QL] The Wave Equation.
   Lecture 22. Pictures. Homework: Section 10.7 # 1, 2-8.
Thursday November 27: Thanksgiving
Tuesday December 2: [QL] Review.
Thursday December 4: Test 3

Tuesday, December 16: Final Test at 9:00 AM in WEL 2.122.




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