Introductory course in linear algebra and differential equations 2019
See HERE for 2020 course
The purpose of this course is to give a brief introduction to linear algebra and ordinary differential equations for incoming two year master students, who don't have the necessary backgrounds or wish a repetition of the subjects. The course is voluntary, but recommended. There is no exam, and no registration (just meet up to class).
- 05. August 2019: The lecture on Friday 9th of August will be held in EL1 in Gamle Elektro.
- 27. June 2019: Welcome to introductory course in linear algebra and differential equations. The course starts at 5th of August.
Timeplan og rom
The lectures and exercises are in EL2 i Gamle Elektro (click for map).
| Monday 5/8 | Tuesday 6/8 | Wednesday 7/8 | Thursday 8/8 | Friday 9/8 | Tuesday 13/8 | Thursday 15/8 | ||
|---|---|---|---|---|---|---|---|---|
| 09.15-10.00 | Lecture | Lecture | Lecture | Lecture | Lecture | Lecture | ||
| 10.15-11.00 | Lecture | Lecture | Lecture | Lecture | Lecture | Lecture | ||
| 11.15-12.00 | Exercise | Exercise | Exercise | Exercise | Exercise | Exercise | ||
| 13.15-14.00 | Lecture | |||||||
| 14.15-15.00 | Lecture | |||||||
| 15.15-16.00 | Exercise |
Lecture Plan
Below is the tentative lecture plan.
Note that you don't need to buy a book for this course, it's only if you want a supplement/reference.
| Topic | Book | Exercises | Lecture notes | Resources | |
|---|---|---|---|---|---|
| Monday 5/8 | Short introduction to sets and functions | Exercise 1 | |||
| Vectors i \(\mathbb{R}^n\) | 7.1, 7.9 (309) | Solution 1 | |||
| Linear transformations from \(\mathbb{R}^n\) to \(\mathbb{R}^m\) | 7.9 (313-315) | ||||
| Matrices | 7.1 | ||||
| Matrix multiplication | 7.2 | ||||
| Systems of linear equations, Gauss elimination | 7.3 | ||||
| Tuesday 6/8 | Vector spaces | 7.9 (309-311) | Exercise 2 | ||
| Linear independence | 7.4 | Solution 2 | |||
| Column-, row- and null space | |||||
| Solutions of systems of linear equations | 7.5 | ||||
| Inverse | 7.8 | ||||
| Wednesday 7/8 | The determinant | 7.6, 7.7 | Exercise 3 | ||
| Eigenvalues and eigenvectors | 8.1 | Solution 3 | |||
| Thursday 8/8 | Transpose, types of matrices | 8.3 | Exercise 4 | ||
| Matrix similarity and diagonalization | 8.4 | Solution 4 | |||
| Matrix exponential | |||||
| Friday 9/8 | Short intro to continuity and differentiability | Exercise 5 | |||
| Differential equations, dynamical systems | 1.1 | Solution 5 | |||
| Phase portrait | 4.5 | ||||
| Existence and uniqueness | 1.7 | ||||
| Tuesday 13/8 | Numerical methods | 1.2 | Exercise 6 | ||
| Separable differential equations | 1.3 | Solution 6 | |||
| Integrating factor | 1.4 | ||||
| Second order differential equations | 2.1, 2.2 | ||||
| Inhomogeneous equations | 2.7 | ||||
| Thursday 15/8 | Linear systems | 4.3 | Exercise 7 | ||
| Duhamels formula | Solution 7 | ||||
| Modeling | 4.2 | ||||
Foreleser
- Navn: Olav Ersland
- Kontor: 1050, Sentralbygg 2
Textbook
- Erwin Kreyszig
Advanced Engineering Mathematics
10th edition
ISBN 0-470-45836-4