Skip Navigation
Jack Baskin School of EngineeringUC Santa Cruz

AM 227 LECTURES, Winter 2020




WARNING: downloading the lecture notes and putting them under your pillow at night will not help you learn the material.

Preparation for the course : This graduate class relies VERY heavily on undergraduate mathematics including

  • Calculus of several variables, including partial differentiation, vector calculus and spherical/cylindrical coordinate systems
  • Concepts of linear algebra
  • Ordinary differential equations
  • Fourier series, Laplace transforms
  • Complex variables
If you do not master these concepts you will really struggle in this course. To prepare for it adequately, make sure you practice by reading and doing examples of Chapter 5 (in particular 5.1, 5.2, 5.3, 5.4, 5.5, 5.6), 10 (in particular 10.7 and 10.9), and 14 (in particular 14.1 and 14.2) of the Riley, Hobson & Bence textbook (see Syllabus page).

This course also relies VERY heavily on everything learned in Partial Differential Equations (AMS212A) and in particular:

  • The method of separation of variables
  • Sturm-Liouville theory
  • The method of characteristics
Please do check on the AMS212A website, including the Syllabus and Lecture notes, that you master the material from that course.



Preparation for each class : You must come to class prepared - just "showing up" is not sufficient. Graduate studies involve independent working practices, and this class is an advanced graduate class.

  • Read the material from the last lecture, and come prepared with questions on what you do not understand. You must be ready to be able to summarize the previous lecture in front of the class.
  • Read the assigned material, and work through it. Come prepared with questions on material you did not understand. The class will assume that you have read the lectures posted online, and you must be prepared to answer questions on them.
  • Read textbooks on the side! Do the suggested homework!
Preparing for class should take you about 2 hours per class. This does not include the homework preparation time.


Week 1:
Week 2:
  • Chapter 2 (part 2)
  • This lecture is pretty simple if you have studied AMS212B, but will require holding on to your socks if you have not. For some lectures on multiscale methods, please see my 212B lecture notes for instance, in this page , Lectures 8 and 9. (Start with the bit about introduction to multiscale)
  • If you are not familiar with the method of characteristics (or don't remember how it works) read up on it, cf. Lectures 13, 14 and 15 in AMS212A page or any graduate PDE textbook, and practice a few simple problems.
Week 3:
Week 4:
Week 5:
Week 6:
Week 7:
Week 8:
Week 9: