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 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