Course syllabus

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Course PM

This page contains the program of the course: lectures and exercise sessions. Other information, such as learning outcomes, teachers, literature and examination, are in a separate course PM.

Program

The schedule of the course is in TimeEdit.

 

Lectures (Mondays and Fridays)

(Observe that on Mondays there are two sessions, morning 8-10 and afternoon 15-17. This is due to the tight schedules of both the students and the teacher. The Monday morning sessions will be most on theory whereas the afternoon sessions will have some examples and problem solving)

Study Week  Chapter  Contents
   1   DM1, K  Introduction, vector spaces, completeness
   2   DM1  Banach spaces, linear mappings, fixed point theory. 
   3   K2  Fixed point theory (cont.), Lp-spaces
   4

 K3.1, 3.4-3.5.

 DM3.1, 

[K].  Lp-spaces (cont.),

[DM] Hilbert spaces
   5   DM4.1-4.7  Linear operators on Hilbert spaces
   6

 DM4.8-4.10,

K4

  Compact operators, spectral theory
   7   DM5, K5  Applications to ODE
   8  Question session

   

    NOT INCLUDED: [DM2], [DM3.5], [DM4.11], [DM5.4-5.7],  [DM5.11-5.12]

 

   Lecture Notes.

                Week 1-2 (a)

                Week 1-2(b) 

      

Exercises (Thursdays) and Recommended exercises

Below is a list of recommended exercises. The exercise classes will be demonstration/discussion of the exercises with *.

 Week  Exercises
   1  DM1: 1, 5, 9*, 13, 28, 30*, 36, 37, 40, 41*, 45
   2  K7.2: 2, 7,11, 12, 13, 17, 18*, 31*, 38
 K7.3: 11, 16, 17, 21*,45, 66, 72, 78*, 89
   3  K7.4: 2, 6, 7*, 10, 14, 16, 17*, 25
   4  K7.5: 9, 10, 11, 12, 15, 19*, 22, 31*, 37*
   5  K7.6: 2, 3*, 4, 5, 6, 9*, 10, 12
   6  K7.6: 14*, 16, 17, 25, 26, 29*, 33, 39.
   7  K7.7: 1(a)(c-d-ef), 1(b)*,  2,  6*, 12, 16, 20*, 25

 

*DMx refers to Chapter x of L. Debnath/P. Mikusinski: Hilbert Spaces with Applications.

**Kx refers to the Chapter x of the lecture notes by P. Kumlin (see the course PM.)

 

Examination

 The exam will consist of solving concrete problems and proving the existing theorems (see below) and proving new theorems using the proved theorems in the course literature. Here is a list of the main theorems whose statements/proofs/applications may appear in the exam.

 

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Computer labs

There are no computer labs in this course. 

Reference literature:

  1. Learning MATLAB, Tobin A. Driscoll. Provides a brief introduction to Matlab to the one who already knows computer programming. Available as e-book from Chalmers library.
  2. Physical Modeling in MATLAB 3/E, Allen B. Downey
    The book is free to download from the web. The book gives an introduction for those who have not programmed before. It covers basic MATLAB programming with a focus on modeling and simulation of physical systems.

 

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Course summary:

Course Summary
Date Details Due