Students should understand the minimal learning outcomes listed on the Math 648 Wiki page.  As evidence of that understanding, students should be able to demonstrate mastery of all relevant vocabulary, familiarity with common examples and counterexamples, knowledge of the content of the major theorems, understanding of the ideas in their proofs, and ability to make direct application of those results to related problems.

1. Second-order elliptic equations
2. Linear Evolution Equations
3. Calculus of Variations
4. Hamilton-Jacobi equations