Methods in Applied Math: APPM 5470 Partial Differential Equations Fall 2007 Lecture Time Room Class 1:00pm-1:50pm ECCR 131 Instructor James H. Curry curry@colorado.edu ECOT 218 Office Hours MW 10:30am-11:30am and Thursday 3:30 to 4:30 (or by appointment) Note: Some of the material covered in this course will also be covered (at a lower level, for example Fourier Convergence Theorems) in APPM 4350/5350. In addition, APPM 5470 overlaps strongly with MATH 5470. Students in either department, APPM or MATH, may register for either course. Text: Required Text: Partial Differential Equations of Mathematical Physics and Integral Equations, R. Guenther and J. Lee (Dover Publications, 1996). Supplementary Reading Matherial: Partial Differential Equations in the 20th Century, Advances in Mathematics, Volume 135, Issue 1, 15 April 1998, Pages 76-144 , Haïm Brezis and Felix Browder, ( Available through the library electronically- Science Direct). Rough Schedule (Very Rough) Chapter 1: Elementary Modeling, X weeks; Chapter 2: First Order PDE's, 2 weeks; Chapter 3: Fourier Series, Strum-Liouville Problems and Conergence, 3 weeks; Chapter 5: Parabolic PDE's, 3 weeks; Chapter 4: Wave Propagation, 2 weeks; Chapter 8, Potential Theory, 2 weeks. Updates and News... No class on Monday September 3rd. Assignment I Assignment I solutions Assignment II Assignment II solutions Assignment III Assignment III solutions Assignment IV Assignment IV solutions Assignment V Assignment V solutions Assignment VI Midterm Midterm solutions Grades, Exams & Homework Grades in the course will be based on 40%-- Homework sets (assigned roughly bi-weekly during the semester); 30%-- Mid-term Exam (to be scheduled in mid October), 7:00pm and 9:30pm, will cover chapters 2 and 3; 30%-- Final Exam: Dec. 17th, 1:30pm to 4:00pm. Rules for the homeworks are as follows. In order to develop complete solutions to the homeworks you may use any reference text from the library. Further, you are encouraged to discuss homeworks problems with other students in the class; and you are even to work on the homeworks together, until you feel comfortable that you understand how to solve and can present solutions to the problem. However, as you expect, each student is required to write up and to submit theirown homework solution set. This means that you are not permitted to copy another student's homework, even if you worked on the problems together. Getting an acceptable grade (B+ to A- range) is easy, do all the work at the 87% to 90% level and show positive growth in understanding the material. In order to receive a grade of A you must impress me that you not only understand the material, but also understand the material at a very high level. This means demonstrating mathematical, computational, and communication skills at a level sufficient for a research pass on the APPM Preliminary Exams. Policies. You are strongly encouraged to review the official CU policy information: Honor Code Disability services Accommodations for religious observances Expectations of classroom behavior Sexual discrimination and harassment Resources Differential Equations Resources Using Maple to solve ODEs Using Mathematica to solve ODEs Numerical ODE solver (Matlab code) For a review of Ordinary Differential Equations see the postscript file LinearODEs.pdf. It is assumed that you have a good working knowledge of the material discussed in this file. Preliminary Information can be found at Syllabi Prelims Here are some old midterm exams ( postscript files) Note that there is no guarantee that the midterm this year will be similar 1991 Midterm 1992 Midterm 1995 Midterm 1996 Midterm 1997 Midterm 2000 Midterm Here are some old final exams ( postscript files) Note that there is no guarantee that the final this year will be similar 1991 Final 1992 Final 1995 Final 1996 Final 1997 Final 2000 Final Useful Formulae, often given with the exams. A Survey (by Professor Segur) of the Phenomena covered in this course.