MA54200 Distributions and Applications

Take-home exam 2

2008-12-04T00:24:00.003-05:00

Problems: 8.12, 8.16, 9.1 from [FJ]
Due: Mon, Dec 15

Homework

2008-11-07T16:49:00.000-05:00

All problems are from [FJ]

#4 Due Fri, Nov 21: 6.3, 7.2, 8.2, 8.4
#3 Due Fri, Oct 31: 4.1, 4.5, 5.2, 5.4
#2 Due Fri, Sep 26: 2.1, 2.3, 2.6, 2.14, 3.3
[Solutions]
#1 Due Fri, Sep 12: 1.3, 1.5, 1.6, 1.9
[Solutions]

Take-home exam

2008-10-03T18:34:00.000-04:00

Problems: 2.5, 3.2, 4.6 from [FJ]
Due: Oct 10, in class

Course Log

2008-09-16T01:30:00.000-04:00

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

Course Information

2008-08-16T18:43:00.000-04:00

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.