Students should understand the topics listed in the minimal learning outcomes on the Math 547 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, and ability to make direct application of those results to related problems, including calculations.
General Cauchy problem
Method of characteristics for first-order equations
Quasilinear systems of conservation laws on a line
Classification of general second-order equations
Canonical forms for semilinear second-order equations