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Math 5440-1
5440-1 home page
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Week 1: Aug 23-27
aug23.pdf 1.1: wave equation derivations and first week homework assignment
aub23b.pdf xeroxed syllabus, supplementary references and partial differential equations lists.
aub23c.pdf data for slinky experiment
aug25.pdf 1.2: closed form solution for wave equation IVP in the upper half plane.
1.1-1.2.pdf first two sections of text, for those of you who don't yet own it.
aug27.pdf 1.2-1.4: solution formulas for wave equation IVP on the real line, and using even and odd extension for IBVP's for an x-interval domain.
Week 2: Aug 30 - Sept 3
aug30.pdf 1.2-1.5: domains of dependence for fixed and free endpoint problems, weak solutions, and the solution to the inhomogeneous wave equation.
maplewaves.mw Maple worksheet illustrating solutions to wave equation IBVP for fixed and free endpoint conditions
maplewaves.pdf pdf copy
sept1.pdf review of the all-dimension FTC, and its consequences
sept3.pdf homework problems for Friday September 10.
Week 3: Sept 8 - Sept 10
sept8.pdf flux integrals, Eulerian and Lagrangian coordinates, and setting up the derivation of Navier-Stokes.
sept10.pdf 2.6: linearity and superposition, as applied to more general IBVP's for the wave equation.
Week 4: Sept 13 - Sept 17
sept13.pdf 2.7: uniqueness theorems and domains of dependence for variable speed wave IBVPs.
sept15.pdf 2.8: classification of 2nd order PDEs in 2 variables.
sept17.pdf 2.8, 3.10: classification of 2nd order PDEs in n variables.
Week 5: Sept 20 - Sept 24
sept20.pdf 3.10-3.11: Laplace's equation
sept22.pdf cont'd
sept24.pdf maximum and comparison principles for Laplace's equation. Also, the homework assignment for Oct 1 - with one additional problem in Monday's notes
Week 6: Sept 27 - Oct 1
sept27.pdf 3.11: A limiting procedure to solve the Dirichlet problem for harmonic functions in the unit Disk using a Riemann sum construction with harmonic measures; also the final hw problem for Oct 1.
sept29.pdf 3.12: heat equation derivation, integral and maximum principle uniqueness arguments.
oct1.pdf 3.12: convolution solutions of heat equation in one space variable.
Week 7: Oct 4 - Oct 8
oct4.pdf Exam 1! (timed to 80 minutes).
exam1sols.pdf solutions.
oct6.pdf Overview of chapter 4: separation of variables.
oct8.pdf Review of Fourier series definition and where it comes from.
Week 8: Oct 18 - Oct 22
oct18.pdf Fourier series continued.
oct20.pdf Fourier series continued - pointwise convergence.
oct22.pdf uniform convergence for Fourier series piecewise C^1 functions, and L^2 convergence for square integrable functions.
Week 9: Oct 25 - Oct 29
oct25.pdf homework for Friday October 29
oct27.pdf 4.22: using Fourier convergence theorems to show that formal solutions to heat equation IBVP's are really solutions.
oct29.pdf 4.23: Boundary value problems for harmonic functions, in rectangles.
Week 10: Nov 1 - Nov 4
nov1.pdf 4.24: Dirichlet problem for harmonic functions in the disk.
nov3.pdf 4.24: cont'd.
nov5.pdf 5.29: inhomogeneous problems for our standard PDE's in two variables.
Week 11: Nov 8 - Nov 12
nov8.pdf 5.29: continued
nov10.pdf : 5.28 Greens functions for 2-point boundary value problems
nov12.pdf 5.27-5.28: variation of parameters solutions for IVP's, and related formulas for Greens function construction.
nov12.2.pdf exam review sheet, and hints of where were heading after the exam.
Week 12: Nov 15 - Nov 19
nov15.pdf exam 2
exam2sols.pdf solutions
nov17.pdf begin Chapter 7 of text by Walter Strauss, "Partial Differential Equations, an Introduction": Divergence theorem identities and the study of harmonic functions and Laplace's equation.
nov19.pdf Chapter 7 continued: Green's functions for the Laplacian.
Week 13: Nov 22 - Nov 24
nov22.pdf finish chapter 7: Dirichlet's Principle.
nov24.pdf overview of the spectral theorem for compact self adjoint operators, and how it will apply to eigenfunctions of the Laplacian.
Week 14: Nov 29 - Dec 3
nov29.pdf the spectral theorem.
dec1.pdf the spectral theorem cont'd.
dec3.pdf application to Laplace eigenfunctions and the Rayleigh-Ritz variational method.
Week 15: Dec 6 - Dec 10
dec6 directory
dec8.pdf course overview
cloaking.pdf Andy's presentation notes on cloaking theory
diffusiontensorimaging.pdf Xiang's presentation notes on tensor diffusion imaging.
quantum.pdf Mike's presentation notes on quantum mechanics.
Week 16: Dec 13 - Dec 17
dec14.pdf final exam!