MATH 435- PARTIAL DIFFERENTIAL EQUATIONS-U.T.K., SPRING 2011- Dr. Alex Freire

Text: Partial Differential Equations: An Introduction, by Walter A. Strauss (2nd. Edition, J.Wiley 2008)

Section 1(20641), MWF 1:25-2:15, Ayres B004

OFFICE HOURS (Ayres 325): by appointment (e-mail to freire@math.utk.edu, or 974-4313): MW 11:00-12:00 and 2:30-3:30

Ch. 1: Introduction

1.1: read independently, try the exercises

W 1/12 Standard examples and boundary conditions (1.3, 1.4)

F 1/14 Well-posed problems (1.5)

Ch.2: Waves and diffusions in 1D

W 1/19 Wave equation on the line (2.1)

F 1/21 Causality and energy (2.2)

M 1/24 Maximum principle for the diffusion equation (2.3)

W 1/26 one-dimensional heat kernel (2.4)

3.1, 3.2: diffusion and wave equations on the half-line: independent reading

Ch. 4,5: Fourier series and boundary-value problems in 1D

F 1/28 separation of variables in 1D: Dirichlet and Neumann BC (4.1, 4.2)

M 1/31 Fourier series (5.1)

W 2/2 Fourier series (5.2, 5.3)

F 2/4 Fourier series: convergence (5.4)

M 2/7 Non-homogeneous BC (5.6)

W 2/9 Review/catch-up

F 2/11 EXAM 1 (Chapters 1,2,4,5,6)

Ch.6: Harmonic functions

M 2/14 Laplaceís equation (6.1)

W 2/16 Rectangles and cubes (6.2)

F 2/18 Poissonís formula (6.3)

6.4 Wedges, annuli, exterior: read independently, try the exercises

Ch.7: Greenís functions

M 2/21 Greenís first identity (7.1)

W 2/23 Greenís second identity (7.2)

F 2/25 Greenís functions (7.3, 7.4)

Ch. 9: Waves and diffusions in 2D, 3D

M 2/28 Energy and causality for the WE (9.1)

W 3/2 WE in spacetime (9.2)

F 3/ 4 Diffusions and Schroedingerís equation (9.4)

M 3/7 WE and diffusions with source terms (parts of 3.4, 9.3, 3.5)

Ch. 10: Boundary-value problems in 2D, 3D

W 3/9 Fourierís method in 2D, 3D (10.1)

F 3/11 WE and diffusions in a 2D-disk (10.2)

3/14 to 3/18: Spring Break

10.4-Nodal sets: independent reading, try the exercises

M 3/21 WE and diffusions in a 3D-ball (10.3)

W 3/23 Bessel and Legendre functions (10.5, 10.6)

F 3/25 Review/catch-up

M 3/28 EXAM 2 (Chapters 6, 7, 9, 10)

Ch. 11: General eigenvalue problems

W 3/30 Minimum property of the eigenvalues (11.1)

F 4/1 Completeness for general domains (11.3)

M 4/4 Symmetric differential operators and Sturm-Liouville (11.4)

W 4/6 Completeness and separation of variables (11.5)

Ch. 12: Distributions

F 4/8 Distributions (12.1)

M 4/11 Greenís functions via distributions (12.2)

Ch. 13: PDE problems from Physics

W 4/13 Electromagnetism (13.1)

F 4/15 Fluids and acoustics (13.2)

M 4/18 Scattering (13.3)

W 4/20 Continuous spectrum and scattering (13.4)

Ch. 14: Nonlinear PDE

M 4/25 Solitons and inverse scattering (14.2)

W 4/27 Calculus of variations (14.3)

F 4/29 Review, catch-up

FINAL EXAM: Thursday, May 5 (Chapters 11,12,13,14)

COURSE POLICIES

1. Attendance: students are expected to come to every class. Each lecture will include new material. While I will take attendance daily for control purposes, there is no mandatory attendance requirement.

2. Course log: This link to the course web page will contain a brief listing of the material covered in each lecture, handouts , announcements and homework problems. It will be updated after every class and should be consulted often. I wonít be using Blackboard.

3. The most important concepts and examples for each topic will be presented in class, but for thorough understanding you are expected to (i) read your textbook and your class notes; (ii) work on the homework problems; (iii) ask questions when there is something you donít understand. I will assume students have read the text in advance, so I can spend most of the lecture on examples and problems. Some sections in the book have been assigned for independent reading.

4. The link classroom behavior expectations includes a list of behaviors considered disruptive (math department policy). Please familiarize yourself with it, as this policy will be enforced. This includes: no laptops, cell phones off, no texting allowed during lecture and no reading extraneous material.

5.HOMEWORK- Homework will be collected and graded each week (about 5 to 8 problems/week).Homework problems posted on the course log by Wednesday are due on Friday, at the start of class. Late homework wonít be accepted.

6. EXAMS- There will be two in-class written exams and a final. All four grades (including the homework grade) will count towards the course grade, with equal weights (25%) Expected grading scale: below 50: F; 50-54: D to C-; 55-69: C or C+ 70-84: B or B+; 85-100: A- to A. I do not `grade on a curveí.

Students with disabilities: please contact the Office of Disability Services (2227 Dunford Hall, 974-6087 V/T) if you need special arrangements for this class.