Integral Equations, Spring 2017

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Integral Equations, Spring 2017

 

Teacher:  Petri Ola

Scope: 10 cr

Type: Advanced studies

Teaching: Weeks 3-9 and 11-18, Monday 10-12 and Wednesday 14-16 in room C122. Easter holiday 13.-19.4.

Topics: This course is an introduction to the theory of linear integral equations. First we briefly study Volterra type equations, and after that move to Fredholm theory. We prove Fredholm's alternative, and give applications to integral equations arising from mathematical physics and applications. There will also be a numerical part of the course worth extra 2 extra credits. More details on the course page: Computational methods for Integral equations.

Prerequisites: Measure and Integral, Differential Equations I and II, Vector Calculus I and II, Topology I, and basics of functional analysis. One should be familiar with the elementary theory of Banach and Hilbert spaces, or then willing to learn the necessary material during the course.

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News

  • Due to work related travel the lecture on Wednesday January 18th is cancelled. The course will however start on schedule, and the first lecture is on Monday, January 16th. 

Teaching schedule

Monday 10-12 and Wednesday 14-16 in room C122. Schedule of the parallel numerical course can be found here.

Exams

The first midterm exam will be on Wednesday, March 8th, 12.15 - 14.45.

Here are the results of the 1st midterm. The first column has has the last four digits of your student number, and the second one has the points you got out of a maximum of 24. Very well done everybody

The second (and last) midterm exam will be on Thursday, May 11th, 12.15-14.45.

Course material

Lecture notes:


Note 06.03.2017 and 04.05.2017: 
Andreas Niskanen has done a wonderful job, and created a Latex-version of the lecture notes. The current version (updated 04.05.2017) is here. Thanks Andreas

Luentomuistiinpanot - osa I (These are from the course given in Spring 2013, you should rotate them 90 degrees counterclockwise )

Lecture notes, part II, again you need to rotate these accordingly. They were also accidentally scanned in reversed order, so you need to read them from the end to beginning

Lecture notes, part III (this contains material about the reduced wave-equation and Sommerfeld radiation condition neededd in HW3)

Lecture notes, from p. 3.15 to the end.

One can also use for example the classic books by K.Yosida: Lectures on Differential and Integral Equations, and R. Kress: Linear Integral Equations.

Summaries of lectures:

Registration


Did you forget to register? What to do?

Exercises

There will be weekly homework assignments which will be returned and graded. The course teaching assistant is  Jonatan Lehtonen. Extra points for the exam can be earned by doing the homework. More details will be explained on the first lecture. The first homework will be handed out on the second lecture week.

Exercises should be returned by 12:00 on Monday, preferably by email to Jonatan Lehtonen (ideally as a PDF-file but images are ok as well, as long as they're readable). You can also hand in paper solutions, either to room B414, during the Thursday exercise session or during the Monday lecture.

Late hand-ins will be accepted but are not encouraged. The absolute deadline is when model solutions are published (which will usually be some time on Monday, so handing in late is risky!). If you need extra time due to illness or something similar, ask beforehand so that the publication of model solutions can be delayed appropriately. =)

Note: The course on numerical methods for integral equations starts next week. Since it will keep you busy, the Homework 5 will be issued only after (or during) the period break 

Exercise sessions

There are two exercise sessions per week:

  • Monday, 12-14, 3rd floor corridor (held by Petri Ola)
  • Friday, 10-12 4th floor corridor (held by Jonatan Lehtonen)

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Week 1