Calculus of Variations PFUG Syllabus
Spring 2005
(subject to change)

A list of suggestions for teaching.

The calculations for the energy of a vector field.

Solutions for the ODE.

Date Topic
1/24 Introductory Comments and Multivariable Calculus Review - Carl
1/26 Explanation of Research Problem/What Does the Energy of a Vector Field Mean?
1/31 Approaches to Minimization/Maximization Problems - Nathan
2/2 Calculations of Energy and Discussion of Results
2/7 Examples of Calculus of Variations Problems - Dan
2/9 Methods to Deal With the Infinite Energy of Our Vector Fields
2/14 Euler-Lagrange Equation - Monroe
2/16 More Vector Field Examples and Possible Ways to Parametrize Them
2/21 Constrained Problems - Emily
2/23 More Calculations and Discussion of Minimizers
2/28 More Constrained Problems - Carl
3/2 A Strange Vector Field Example
3/7 Spring Break-No Class
3/9 Spring Break-No Class
3/14 Extermal Surfaces - Nathan
3/16 Looking at the PDEs Euler-Lagrange Gives Us
3/21 More Extremal Surfaces - Dan
3/23 We Have Some PDE Solutions
3/28 Let's Talk About These New PDE Solutions
3/30 We Have Some Answers
4/4 Using Euler-Lagrange in Physics Settings - Monroe
4/6 Assessing What We Want To Do Now
4/11 More Discussion of Physics and Hamilton's Principle - Emily
4/13 A Field Trip to See What the Other Vigre PFUGs Do
4/18 Research
4/20 The Nonexistence of Smooth Nonzero Vector Fields on the Sphere
4/25 ??
4/27 Research
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