Syllabus

AMS 211 is a review of the undergraduate mathematics that you will need to have mastered going forward in your graduate studies. The full list of topics is listed below. It is expected that most, if not all of the students have already studied most, if not all of this material. With this expectation, we move through the material very quickly! To succeed, you wil need to read ahead and work on the homework assiduously. The quarter will be over before you know it. 

We are using Mathematical Methods for Physics and Engineering, by Riley, Hobson and Bence as the textbook for the course. The homework assignments all come from this book, and the chapters refered to below are from this book. Other textbooks you may find useful as references include

• Arfken, G., "Mathematical Methods for Physicists", Academic Press
• Strang, G., "Introduction to Applied Mathematics", Wellesley Cambridge Press
• Courant, R. & Hilbert, D., "Methods of Mathematical Physics", Wiley Interscience.

We will study the following topics in the order listed, according to the (approximate) schedule below:

• Chapter 5: Partial derivatives. 2-3 lectures.
• Chapter 6: Multiple integrals. 2-3 lectures.
• Chapter 8: Matrices and vector spaces. 4 lectures.
• Chapter 10: Vector calculus. 3-4 lectures.
• Chapter 11: Line, surface and volume integrals. 3 lectures.
• Chapter 12: Fourier series. 2-3 lectures.
• Chapter 13: Integral transforms. 2-3 lectures.
• Chapters 24-25: Complex analysis. 3 lectures.
• Chapter 14: First order ODE.s. 2-3 lectures.
• Chapter 15: Higher order ODE.s. 2-3 lectures.
• Additional topics if time permits.

Grading: Your grade will be based on two take-home midterm exams (50%) and the final exam (50%). 

Comments: 

• The first take-home midterm will cover chapters 5, 6, 8 and 10.

• The second take-home midterm will cover chapters 11, 12, 13 and 24-25. 

• The final exam will be held on Wednesday, Dec 9, 8:00 - 11:00 am. 

• The final exam will be based in part on the homework assignments.