Exam 1: Wednesday, Feb. 18 --Room 636 SEO -- note change!!!

Review Class - Friday, Feb. 13 - 12-1 in 310 AH

Tentative Topics - all material covered in class unless specifically omitted

1. Chapter 1 - heat equation; flux and Fourier's law; boundary conditions (no derivations needed); equilibrium temperature distribution; polar coordinates.
2. Chapter 2 - Formulation of well-posed problem; SOV; BVP; Fourier series (sine and cosine series); Laplace's equation.
3. Chapter 3 - more Fourier series; periodic extension; odd and even extension; Gibb's phenomenon; eigenfunction expansion method.
4. Chapter 4 - wave equation - formation, boundary conditions, SOV solution, standing waves
5. Chapter 5 - Sturm-Liouville BVP; key results (p. 163); self-adjoint operator; Lagrange and Green's identity; boundary conditions of the third kind.

Exam 2: Friday, April 2 -- Room 636 SEO -- tentative!!!

A sheet of formulas from the front cover of text and the Fourier transform table from the back cover will be distributed with the exam.

Tentative Topics - all material covered in class unless specifically omitted

1. Chapter 7 - separation of time variable - heat and wave equation; Helmholtz equation - solving and results; Green's 2nd identity; circular domain problems - Bessel functions; omit - cylindrical coordinates
2. Chapter 8 - equilibrium (steady-state) solutions; eigenfunction expansion method; converting nonhomogeneous bc's to homogeneous; solving pde's with nonhomogeneous bc's directly; wave equation and resonance; Poisson's equation.
3. Chapter 9 - Construct Green's function directly for ODE with delta function - jump condition formuation and eigenfunction expansion; Green's function and nonhomogeneous bc's; Fredholm alternative theorem (skip Generalized Green's function); Green's for Poisson's equation; free-space Green's function.
4. Chapter 10- Fourier transform; solving PDE's in domains of infinite extent.

Tentative Topics - all material covered in class unless specifically omitted

1. Chapter 9 - Construct Green's function directly for ODE with delta function - jump condition formuation and eigenfunction expansion; Green's function and nonhomogeneous bc's; Fredholm alternative theorem (skip Generalized Green's function); Green's for Poisson's equation; free-space Green's function.
2. Chapter 10- Fourier transform; solving PDE's in domains of infinite extent.
3. Green's function for heat equation (11.3)
4. Method of characteristics (12.2); wave equation, D'Alembert's solution, charactistics; semi-infinite string and reflections (12.3,12.4)
5. Chapter 13 - Laplace transform, review, (13.2,13.3); wave equation and heat equation (13.4)