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



  • Erwin Kreyszig
    Advanced Engineering Mathematics
    10th edition
    ISBN 0-470-45836-4
2020-08-12, Matthew Tandy