MATH 656 PROBLEM ASSIGNMENTS

Homework Exercises

The exercises make you familiar to the fundamental concepts and basic techniques and deepen your understanding. Their importance can never be over-emphasized. Your analytical skill and conceptual understanding gained through homework exercises will be tested on exams. If you are uncomfortable with how to solve any of these kinds of problems, please seek help either from your fellow students or from the instructor.

Guidelines for solving problems

Write up your work clearly! It at least saves your time upon review.
Be deliberate when solving problems! Make every step consciously and think about why it is a step in the right direction. After doing this for a while you will realize that you have developed new useful reflexes.
Once you have solved a problem, list the ideas you have used and decide whether the answer is reasonable BEFORE looking at answers from other sources.
You are encouraged to do some work in groups. Explaining ideas to other people helps clarify them for you too. But you need to finish and turn in your own assignment separately.

Soblev Spaces
HW #1: Problems 1—18, pages 289—292.
Assignment #1: problems 7, 11, 12, 13, 18. Due Feb. 07

Second-Order Elliptic Equations
HW #2: Problems 1—10, pages 345—347.
Assignment #2: problems 1, 2, 3, 5, 7, 8, 10.

Linear Evolution Equations
HW #3: Problems 1—15, pages 425—427.
Assignment #3: / problems 1, 2, 3, 4, 6, 7, 9, 10.

The Calculus of Variations
HW #4: Problems 1—13, pages 486—490.
Assignment #4: / problems 1, 2, 3, 8, 11, 12, 13. Due April 06

Non-variational Techniques
HW #5: Problems 1—9, pages 536—538.
Assignment #5/ problems 1, 2, 4, 5, 7.

Hamilton-Jacobi equations
HW #6: Problems 1—5, pages 563—564.
Assignment #6 / problems 1, 2, 4, 5.

Systems of Conservation Laws
HW #7: Problems 1—6, pages 611—612.
Assignment #7 / problems 1, 3, 4, 6.