Course Announcement
**MATH 655 Partial Differential
Equations I** Fall 2016

**Instructor**: P.
Sacks, 436 Carver psacks@iastate.edu Office Hours: MF 2-3, TR 11-12

**Class
meeting time/place**: TR 9:30-10:45, 031 Ross Hall

**Textbook**: *Partial Differential Equations, 2 ^{nd}
ed. *by L. C. Evans

**Prerequisites**:
MATH 515 or MATH 519 or consent of the instructor

**Course
description**: Introduction to the theory of partial
differential equations at the advanced graduate level. The principal concerns are
existence, uniqueness and regularity of solutions, methods for representation
of solutions and interesting qualitative properties.

**Course
Outline**:

I.
Study of model linear problems

a. Transport
equation

b. Laplace
equation

c. Heat
equation

d. Wave
equation

II.
Nonlinear first order equations

a. Method
of characteristics

b. Scalar
conservation laws

III.
Special methods

a. Separation
of variables

b. ODE
methods – plane wave, travelling wave and similarity solutions

c. Integral
transform methods

d. Useful
changes of variable

IV.
General theory of linear PDEs of arbitrary
order

a. Fundamental
solutions

b. Local
solvability – Malgrange-Ehrenpreis and Cauchy-Kowalewski theorems, Lewy example

c. Hypoellipticity

d. Wave
front sets

Items I-III correspond roughly
to Chapters 1-4 in the text. MATH 656, the Spring 2017
continuation of the course, will cover material from Chapters 5-9, specifically
Sobolev spaces, general theory of linear elliptic,
parabolic and hyperbolic PDEs of second order, and introduction to techniques
for the study of nonlinear PDEs.

The course grade will be based on 6-7 homework
assignments. Click here for homework assignments.

**Other
References:**

*Methods of Mathematical Physics, Volume II*by R. Courant and D. Hilbert*Introduction to Partial Differential Equations*by G. Folland*Partial Differential Equations*by F. John*The Analysis of Linear Partial Differential Operators, I-IV,*by L. Hörmander*Partial Differential Equations: Methods and Applications*by R. McOwen*Partial Differential Equations*by J. Rauch*Basic Linear Partial Differential Equations*by F. Treves*Partial Differential Equations: An Introduction*by W. Strauss

If a student has a disability that qualifies under the Americans with Disabilities Act and Section 504 of the Rehabilitation Act and requires accommodations, he/she should contact the Disability Resources (DR) office for information on appropriate policies and procedures. DR is located on the main floor of the Student Services Building, Room 1076; their phone is 515-294-7220.