# Introductory course in linear algebra and differential equations 2020

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) | Solutions 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 4/8 | Vector spaces | 7.9 (309-311) | Exercises 2 | ||

Linear independence | 7.4 | Solutions 2 | |||

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 | Solutions 3 | |||

Thursday 6/8 | Transpose, types of matrices | 8.3 | Exercises 4 | ||

Matrix similarity and diagonalization | 8.4 | Solutions 4 | |||

Matrix exponential | |||||

Friday 7/8 | Short intro to continuity and differentiability | Exercises 5 | |||

Differential equations, dynamical systems | 1.1 | Solutions 5 | |||

Phase portrait | 4.5 | ||||

Existence and uniqueness | 1.7 | ||||

Tuesday 11/8 | Numerical methods | 1.2 | Exercises 6 | ||

Separable differential equations | 1.3 | Solutions 6 | |||

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 | Solutions 7 | |||

Duhamels formula |

### Foreleser

- Navn: Matthew Tandy
- Kontor: 1144, Sentralbygg 2

### Textbook

- Erwin Kreyszig

Advanced Engineering Mathematics

10th edition

ISBN 0-470-45836-4