PART I-INTEGRAL EQUATIONS
1. Intro.to Int.Eqs.
10. Symmetric Kernels
2. Volterra Eq.
11. Gx,t)for Higher Order Operators
3. Sol.by Neumann Series
12. Fredholm's Sol.of his Eq.
4. Difference Kernels
13. Homogeneous Fredholm Eq.
5. Fredholm Int.Eqs.
14. Eigenvalue Determination
6. Pincherle-Goursat Kernels
15. Solution by Iteration
7. Num.Sol.to Fredholm Eqs.
16. Sturm-Liouville Theorem
8. BVP's & Greens Functions
17. Hilbert-Schmidt & the Bilinear Formula
9. Construction of G(x,t)
18. Singular Integral.Eqs.
PART II-CALCULUS OF VARIATIONS
19. First Prob.in Calculus
28. First Var.with Constraints
of Variations
29. Prob.of Dido,Catenary
20. Brachistochrone Problem
30. Min.Volume for Fixed
21. Min.Surface of Revolution
Surface Area
22. Fermat Principle
31. Rayleigh-Ritz Variational
23. Optical Fibers&Snells Law
for Finding Eigenvalues
24. Geodesics
32. Lagrange Multipliers
25. Newton's Min.Drag Prob.
33. Applications of LM's
26. Lagrange Eqs.of
34. Second Variation to Deter-
27. Prob.of Plateau
mine Max or Min Conditions
Grade Determination:3
Class exams at 25% each, plus weekly homework for the
remaining 25%. No final exam or required text. For side reading look
at-
(1)Tricomi"Integral Equations"Interscience
(2)Weinstock"Calculus of Variations", McGraw-Hill
.
Homework assignments and supplemental material will be posted on this
WEB site.