# 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 Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture Lecture 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

### Textbook

• Erwin Kreyszig