# MA54200 Distributions and Applications

Purdue University Fall 2008

## Thursday, December 4, 2008

## Friday, November 7, 2008

## Friday, October 3, 2008

## Tuesday, September 16, 2008

### Course Log

**Planned**

*Wed, Sep 17*: §2.8 Duality, §3.1 Continuous linear forms and distributions with compact support.

**Covered**

*Mon, Sep 15*: §2.6 Linear differential operators, §2.7 Division in

*D'*(

**R**)

*Fri, Sep 12*: §2.4 Primitives in

*D'*(

**R**), §2.5 Product of a distribution and a smooth function

*Wed, Sep 10*: §2.2 Some examples (cont) §2.3 A distribution by analytic continuation

*Mon, Sep 8*: §2.1 The derivatives of a distribution, §2.2 Some examples.

*Fri, Sep 5*: §1.4 Localization, §1.5 Convergence of distributions

*Wed, Sep 3*: §1.3 Distributions of finite order; §1.4 Localization, partition of unity

*Fri, Aug 29*: §1.2 Convolutions, Theorem 1.2.1; §1.3, Theorem 1.3.1

*Wed, Aug 27*: §1.2 Test Functions; §1.3 Distributions, Theorem 1.3.2

*Mon, Aug 25*: Intro, §1.1

## Saturday, August 16, 2008

### Course Information

**Schedule:**MWF 12:30 - 1:20pm in MATH211

**Instructor:**Arshak Petrosyan

*Office Hours:*MWF 10:30 -11:30am, or by appointment, in MATH610

**Textbook:**

[FJ] F. G. Friedlander and M. Joshi,

*Introduction to the Theory of Distributions*, Cambridge University Press, 2nd edition.

**Prerequisite:**MA544 and a knowledge of linear algebra

**Course Description:**

The theory of distributions is an extension of classical analysis dealing with the most general notion of differentiability. It is of particular importance in partial differential equations (PDEs) and has applications in virtually every field of modern analysis. This is an introductory course where we will study the basic properties of distributions, convolutions and Fourier transforms, Sobolev spaces, as well as applications to PDEs.

**Homework:**There is going to be a homework assignment due every other Friday. Assignments will be posted on this page.

**Exams:**We will have a (take home) midterm exam as well as a final.