# Introductory course in linear algebra and differential equations 2019

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).

**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