Math 512:  Introduction to Integral Equations

Spring 2014

 

Peter Golubtsov
Professor of Mathematics
Lomonosov Moscow State University

Visiting Professor
Department of Mathematical Sciences
The University of Montana

 

Syllabus:  IE Syllabus Spring 2014.pdf

Course Description:  M512 - Introduction to Integral Equations.pdf

To view a video recording of a lecture, right-click on the link to save it to your computer. Once it is downloaded, you will be able to watch the lecture without interruption.

Date

Lecture

Topic

Handouts

Videos

Jan. 27

1

Introduction, Examples

01

01

Jan. 29

2

Metric and Normed Spaces

02

02

Jan. 31

3

Normed and Inner Product Spaces

03

03

Feb. 3

4

Examples.  Linear Operators

04

04

Feb. 5

5

Linear Operators in Normed Spaces

05

05

Feb. 7

6

Bounded Operator.  Compact Operator. 
Homework #1 Due Feb. 14
(or Feb. 21)

06

06

Feb. 10

7

Compactness of Fredholm Operator

07

07

Feb. 12

8

Existence of Eigenvalues for Compact Operator

08

08

Feb. 14

9

Eigenvalues and Eigenvectors of Compact Operator

09

09

Feb. 19

10

Eigenvalues and Eigenvectors of Fredholm Operator

10

10

Feb. 21

11

Characteristic values and Eigen functions of Fredholm Operator.  Degenerate kernel.
Homework #2 Due Mar. 7

11

11

Feb. 24

12

Characteristic values and Eigen functions Examples

12

12

Feb. 26

13

Examples.  Hilbert-Schmidt Theorem

13

13

Mar. 3

14

Hilbert-Schmidt Theorem

14

14

Mar. 5

15

Fredgolm Equation of Second Kind with Symmetric Kernel

15

15

Mar. 7

16

Fixed Point Theorems

16

16

Mar. 10

17

Fredholm Equation with “small” lambda.

17

17

Mar. 12

18

Volterra Equation.

18

18

Mar. 14

19

Volterra Equation. Resolvent.

19

19

Mar. 17

20

Volterra Equation: Problems.

Homework #3 Due Mar. 28

20

20

Mar. 19

21

Fredholm Equation with Degenerate Kernel. Resolvent.

21

21

Mar. 21

22

Adjoint Fredholm Equation.

22

22

Mar. 24

23

General Fredholm Equation of Second Kind.

23

23

Mar. 26

24

Fredholm Theorems. Examples.

24

24

Mar. 28

25

Examples.

25

25

Apr. 7

26

More Examples.

Homework #4 Due Apr. 21

26

26

Apr. 9

27

Sturm-Liouville Theory. Introduction.

27

27

Apr. 11

28

Green’s Function.

28

28

Apr. 14

29

Comments on Homeworks 2 & 3. 

Green’s Function Example.  Sturm-Liouville Problem.

29

29

 


Last modified: 14-April-2014
Mail comments to:  peter.golubtsov@umontana.edu