Math 797 Calculus of Variations
Instructor: Matthew Dobson
Class meeting time: MWF 10:10-11:00am
Location: LGRT 1114
Course Text: Introduction to the Calculus of Variations by B. Dacorogna
Office hours: TBD.
Office: LGRT 1430 (Tower)
e-mail: dobson@math.umass.edu
Office phone: 545-7194
Course Structure and Grading Policies:
- The course grade will be a combination of participation, homework,
and a single presentation.
- There will be four or five homework assignments during the semester. You are encouraged to work together.
- Each student will be responsible to read and present
a topic related to the course material during class.
- The course grade will be a combination of course participation, homework
assignments, and the project. There are no exams in the course.
Homework
Homework 1: Due 2/15
From the text:
1.2.1, 1.3.1 parts ii) and iii), 1.4.1 part i)
Homework 2: Due 3/8
From the text:
2.2.4, 2.2.8
Homework 3: Due 3/25
- Summarize the work of Chapters 3 and 4 into a single theorem for the 1D case. Include both minimal assumptions for minimizers as well as the additional assumptions necessary for uniqueness and increased regularity.
- Find examples which demonstrate the need for the additional hypotheses, particularly
- Where a minimizer exists, but is not unique
- Where a unique minimizer exists, but it is not smooth enough to satisfy
an Euler-Lagrange Equation
Reading and Summaries
Week 1/22: Read Chapter 0 and Sections 1.1 and 1.2.
We gave an overview of the direct methods approach and example problems
before reviewing background material.
Week 1/28: Read Sections 1.3-1.5.
Week 2/4: Read Sections 2.1-2.2.
Week 2/11: Read Sections 2.3-2.5.
Week 2/18: Read Sections 3.1-3.3.
Week 2/25: Read Sections 3.1-3.3.
Week 3/4: Read Sections 3.4, 4.1 and 4.2.