EGM6323-PRINCIPLES OF ENG. ANALYSIS III
Instructor-U.H.Kurzweg; Class meets MWF 2nd Period (9:30-10:45am), 3Credits.

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.