## Differential Equations, Spring 2013 (Diff)

See also the Study Information System
SIS page
and (requires login)
Absalon.

### LECTURES

There are lectures by H. Schlichtkrull, Mondays 13:15-15:00 in Aud 7 and Wednesdays, 9:15-12:00 in Aud 8.

For this course the lecture notes *Ordinary Differential Equations; An Introduction for Mathematicians* by Jacob Schach Møller are used. ISBN 9788770782906.
Note that it is a revised edition compared to the one used in 2012.

Below is the plan for the lectures.

**Week 1**, Monday 4/2: 1.1, 1.2, 1.3 (only to p 13, top), 1.4 (to p 17, top).

**Week 1**, Wednesday 6/2:
note 1,
2.1, 2.2, 3.1, 3.2 (to p 58), 3.3 (n=1).

.

**Week 2**, Monday 11/2: Note 1 (Example 3.10), 3.3 (n>1), 3.4 (to p 68), 5.1 (to p 108)

**Week 2**, Wednesday 13/2: 5.2, 5.3, 6.1, Appendix A.4

**Week 3**, Monday 18/2: 6.1, 6.2, 6.5 (to p 165)

**Week 3**, Wednesday 20/2: 6.4, 6.5 (rest), 7.1 (only p 184), 7.2 (to p 186)

**Week 4**, Monday 25/2: 7.2 (rest), 7.3

**Week 4**, Wednesday 27/2: 8.1, 8.2 (Prop 8.6. Skip p 208 mid-211 mid).

**Week 5**, Monday 4/3: 8.2 (Thm 8.11), 8.3.

**Week 5**, Wednesday 6/3: Solution by power series.
See the notes
(the notes have been revised on March 7)

**Week 6**, Monday 11/3: Summary of Fourier theory.
See the notes

**Week 6**, Wednesday 13/3:
Partial Differential Equations (PDE).
See the notes
(an expanded version has been uploaded March 12)

**Week 7**, Monday 18/3: More PDE's. See the notes
(some corrections were added on March 18).

**Week 7**, Wednesday 20/3: The hydrogen atom.
See the notes
(some corrections were added on March 20)

**Week 9**, Tuesday 9/4: There is an opportunity to ask questions, 10:15-?, Auditorium 8.

Here is a list of the "pensum" (curriculum).

### EXERCISE CLASSES

There are exercise classes by Mads Christian Hansen
(m08mch snabela math punktum ku punktum dk).
Written solutions by Mads to some of the exercises can be found
here
(use the pull down menu under "Diff").

Mondays,
15:15-17:00 in A106 and Wednesdays 13:15-15:00 in 1004 (DIKU).

**Week 1**, Monday 4/2: No class

**Week 1**, Wednesday 6/2: 1.2 a3,a4; 1.5; 1.7; 1.10 - 2,4,6; 1.11; 1.18; 1.19; 1.25

**Week 2**, Monday 11/2:
2.2; 2.3; 2.9; 3.1; 3.4; 3.7; 3.10 (see Note 1)

**Week 2**, Wednesday 13/2:
4.9; 4.11; 4.19, the first equation
(solve the exercises from Chapter 4 with the method of Section 3.2); 5.1; 5.4 a; 5.12

The first assignment is to be handed in at the
start of the exercise class.

**Week 3**, Monday 18/2: 5.23 1; 6.3; 6.7; 6.9 but without using Example 6.9;
an extra exercise 1

**Week 3**, Wednesday 20/2:
6.1; 6.4; 6.5 (Hint for b: Show that the decreasing chain of subspaces,
obtained by successive applications of A to R^n,
is strictly decreasing); 6.14; 6.17; 6.32;

The second assignment
is to be handed in at the start of the exercise class.

**Week 4**, Monday 25/2:
An extra exercise 3; 7.8; 7.9; 7.10; 7.16.

(there is no extra exercise 2)

**Week 4**, Wednesday 27/2:
6.33; 7.12; 7.13; 7.20; 7.21

The third assignment
is to be handed in at the start of the exercise class.

You can see an exam from last year here.

**Week 5**, Monday 4/3:
8.1; 8.2; 8.3; 8.5; extra exercise 4

**Week 5**, Wednesday 6/3: 8.13; 8.16; 8.17; 8.19;
extra exercise 5.

The fourth assignment is to be
handed in at the start of the exercise class.

**Week 6**, Monday 11/3: Exercises on power series
here

**Week 6**, Wednesday 13/3:
Some exercises on Fourier series.

The fifth assignment is to be handed in at the start of the exercise class.

There is a written assignment for Wednesday 20/3.

**Week 7**, Monday 18/3: The exercises in todays
notes

**Week 7**, Wednesday 20/3: The exercises in the notes on the hydrogen atom.

The sixth assignment is to be handed in at the start of the exercise class.

**Week 8**, Wednesday 3/4, 13:15-15, room A 106. Last years exam.

### WRITTEN ASSIGNMENTS

There are weekly written assignments (non mandatory):

Assignment 1 for Wednesday 13/2.

Assignment 2 for Wednesday 20/2.

Assignment 3 for Wednesday 27/2.

Assignment 4 for Wednesday 6/3.

Assignment 5 for Wednesday 13/3.

Assignment 6 for Wednesday 20/3.

SOME SOLUTIONS:

Here is a solution
to Assignment 1.

Here is a solution
to Assignment 2.

Here is a solution
to Assignment 3.

Here is a solution
to Assignment 4.

Here is a solution
to Assignment 5.

Here is a solution
to Assignment 6.

### EXAM

The exam is on Wednesday, April 10 2013, from 9 until 12 (3 hours). See the
location
(in Danish).

The exams from last year first and second.