Introductory course in linear algebra and differential equations 2020
See HERE for 2021 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).
Timeplan and room
The lectures and exercises are in EL6 i Gamle Elektro (click for map).
| Monday 3/8 | Tuesday 4/8 | Wednesday 5/8 | Thursday 6/8 | Friday 7/8 | Tuesday 11/8 | Wednesday 12/8 | ||
|---|---|---|---|---|---|---|---|---|
| 09.15-10.00 | Lecture | Lecture | Lecture | Lecture | Lecture | Lecture | Lecture | |
| 10.15-11.00 | Lecture | Lecture | Lecture | Lecture | Lecture | Lecture | Lecture | |
| 11.15-12.00 | Exercise | Exercise | Exercise | Exercise | Exercise | Exercise | 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 3/8 | Short introduction to sets and functions | Exercises 1 | |||
| Vectors i \(\mathbb{R}^n\) | 7.1, 7.9 (309) | ||||
| 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 4/8 | Vector spaces | 7.9 (309-311) | Exercises 2 | ||
| Linear independence | 7.4 | ||||
| Column-, row- and null space | |||||
| Solutions of systems of linear equations | 7.5 | ||||
| Inverse | 7.8 | ||||
| Wednesday 5/8 | The determinant | 7.6, 7.7 | Exercises 3 | ||
| Eigenvalues and eigenvectors | 8.1 | ||||
| Thursday 6/8 | Transpose, types of matrices | 8.3 | Exercises 4 | ||
| Matrix similarity and diagonalization | 8.4 | ||||
| Matrix exponential | |||||
| Friday 7/8 | Short intro to continuity and differentiability | Exercises 5 | |||
| Differential equations, dynamical systems | 1.1 | ||||
| Phase portrait | 4.5 | ||||
| Existence and uniqueness | 1.7 | ||||
| Tuesday 11/8 | Numerical methods | 1.2 | Exercises 6 | ||
| Separable differential equations | 1.3 | ||||
| Integrating factor | 1.4 | ||||
| Second order differential equations | 2.1, 2.2 | ||||
| Inhomogeneous equations | 2.7 | ||||
| Wednesday 12/8 | Linear systems | 4.3 | Exercises 7 | ||
| Modeling | 4.2 | ||||
| Duhamels formula |
Foreleser
- Navn: Matthew Tandy
- Kontor: 1144, Sentralbygg 2
Textbook
- Erwin Kreyszig
Advanced Engineering Mathematics
10th edition
ISBN 0-470-45836-4