# 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).

• 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 Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Exercise Exercise Exercise Exercise Exercise Exercise Lecture Lecture 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

### Textbook

• Erwin Kreyszig