Math 4250 (Partial Differential Equations) Spring 2024

Instructor: Ching-Li Chai
Office: DRL 4N36, Ext. 8-8469.
Office Hours: MW 11:20-12:00, and by appointments.
Email: chai@math.upenn.edu

TA/Grader: Yaojie Hu
Office: DRL 3C17
Office Hours:
Email:yaojie@sas.upenn.edu

Homework Assignments

General Information

• Lectures: MW 12:00-1:29 pm, DRL 3C8
  First meeting: Monday, January 22.
  
  
• Textbook:
  • Walter Strauss, Partial Differential Equations, second edition, John Wiley and Sons, 2008, is the "official textbook". Many problems in homework assignments are from this book.
    Corrections to Strauss, Partial Differential Equations, second edition
  • Stanley Farlow, Partial Differential Equations for Scientists and Engineers, Dover republication of the 1982 edition by John Wiley and Sons. An elementary text organized into 46 lessons. A September 2000 SIAM review by J. David Logan had the following comments: "Beginning students will like the easily digestible outline form of each lesson, where the main point is reached quickly and without ado."
  • Yehuda Pinchover and Jacob Rubinstein, An Introduction to Partial Differential Equations CUP 2005 and Rustum Choksi, Partial Differential Equations, a first course are two supplementary texts at the same level of Strauss, where you can find alternative treatments.
  
  
• Brief course description:
  
  
• Prerequisites: Math 2400 or its equivalent. Some knowledge of real analysis and writing proofs, as in Math 3600/5080.
  
  
• Homework will be assigned every week, posted on the course website. You will have (at least) a week before an assignment is due. You can submit your work either by uploading a pdf file to Canvas, or by putting a hard copy in the mailbox of your TA/grader. It will be great if you submitted work is generated by a computer program such as LaTeX; otherwise please make sure that the scanned pdf file of your handwriting is clearly and easily legible. Collaboration between students is encouraged, but you must write your own solutions, understand them and give credit to your collaborators. (To be precise, put a list of the students with whom you collaborated on your homework.)
  Late homework will not be accepted. Your two lowest homework scores will be dropped.
  
  
• Exams: There will be three (3) in-class exams.
  
  
• Attendance and Course Notes: It is in your best interest to attend each lecture and take accurate notes. You will be tested on the material as it is covered in class. If you miss a lecture, make sure that you copy from a classmate and review the notes from that day.
  
  
• Evaluation: Your course grade is based on: your level of participation in class (10%), homework (24%), as well as the in-class exams (22% each).
  
  

Important Dates:

• First meeting of classes: Monday, January 22
  
• First in-class exam: Wednesday, February 21.
  
• Drop period ends: Tuesday, February 27
  
• Spring break: March 2 (Saturday)-10 (Sunday)
  
• Second in-class exam: Wednesday, March 27
  
• Last day to withdraw: Tuesday, April 2
  
• Third in-class exam: Wednesday, May 1
  
• Last day of classes: Wednesday, May 1
  

Some References and supplementary texts:

• Ockendon, Howison, Lacey and Movchan, Applied Partial Differential Equations, revised edition, OUP 2003. A treatment of the standard topics by practicing applied mathematicians, from a modern perspective. The level of maturity required is between typical undergraduate and graduate students. Theorems are not formally stated or proved as in usual mathematics textbooks.
• R. Courant and D. Hilbert Methods of Mathematical Physics, vol I, 1953; vol II, 1962. A classic in every sense. Volume I is a masterpiece in classical mathematics, where the traditional equations are introduced via calculus of variations. Contains treatments of integral equations, spectral properties the Laplacian on bounded domains and Weyl's law, and special functions which are needed when one wants to write down explicit solutions of classical boundary value problems by the method of separation of variables. Volume II is the most successful textbook on PDE ever written.
• P. Morse and H. Feshbach Methods of Theoretical Physics, 2 volumes, McGraw Hill, 1953. A monumental treatment of PDE for physicists and engineers who need explicit solutions, reminiscent of the "German handbook" tradition. It is the PDE textbook and bible on solving classical PDEs for generations of physicists. (In later years physics graduate students learn analytic techniques for solving classical PDEs from Jacson's Classical Electrodynamics.) For a more succinct (289 pages, not counting exercises and hints of solutions) treatment for physicists, see volume V of Arnold Sommerfeld's Lectures on Theoretical Physics.
• V. I. Smirnov, A Course of Higher Mathematics, Volume 4, Integral and Partial Differential Equations. The approach is similar to Morse and Feshbach, but more mathematical. For a more concise (about a quarter of the length) treatment in the same spirit, see Petrovsky's Lectures on Partial Differential Equations, Dover.
• L. Evans, Partial Differential Equations, an excellent graduate level textbook on PDE.
• References on special functions:
  • Whittaker and Watson, A Course of Modern Analysis, a timeless classic. Part I contains basic complex analysis (and more), while Part II treats special functions.
  • Chapter 7 of Courant and Hilbert volume I.
  • NIST Handbook on Mathemtical Functions, available online from NIST website.
  • N. N. Lebedev, translated and edited by R. Silverman, Special Functions and Their Applications, Dover, 1972.
  • I. S. Gradshteyn and I. M. Ryzhik, Table of Integrals, Sieries and Products, translated and edited by A. Jeffrey, Academic Press.