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

*Text: *Partial Differential Equations: An Introduction, by Walter A. Strauss (2^{nd}. 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 Laplace’s equation (6.1)

W 2/16 Rectangles and cubes (6.2)

F 2/18 Poisson’s formula (6.3)

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

Ch.7: Green’s functions

M 2/21 Green’s first identity (7.1)

W 2/23 Green’s second identity (7.2)

F 2/25 Green’s 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 Schroedinger’s 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 Fourier’s 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 Green’s 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 won’t 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 don’t 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 won’t 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 curve’. *

*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.