# Introductory course in linear algebra and differential equations (2022)

Welcome to the introductionary course in linear algebra and ordinary differential equations

I have given a lot more problems than I expect you to do. Prioritise, and please do not try to do them all.

The course is voluntary with no exam.

## Schedule:

The course will be held in August 2022, in week 32 (August 8th – 12th) and in week 33 (August 16th – 19th). Map to the rooms: EL1 and F2.

Monday 8/08 | Tuesday 9/08 | Wednesday 10/08 | Thursday 11/08 | Friday 12/08 | |
---|---|---|---|---|---|

Room | EL1 | EL1 | EL1 | EL1 | EL1 |

09:15-10:00 | Lecture | Lecture | Lecture | Lecture | Lecture |

10:15-11:00 | Problem session | ||||

11:15-12:00 | Problem session | Problem session | Problem session | Problem session | |

Monday 15/08 | Tuesday 16/08 | Wednesday 17/08 | Thursday 18/08 | Friday 19/08 | |

Room | F2 | F2 | F2 | F2 | |

09:15-10:00 | No lecture! (Matriculation Ceremony) | Lecture | Lecture | Lecture | Problem session |

10:15-11:00 | |||||

11:15-12:00 | Problem session | Problem session | Problem session |

The web page from last year can be consulted to see the main elements. We will however not be following the exact same recipe, nor have the exact same curriculum.

## Course contents

The focus in our course will be on ordinary differential equations (ODE), and mostly on linear ODE's with constant coefficients. Towards the end we will look at systems of differential equations.

Linear algebra will also be touched upon in order to study systems of differential equations, but also on its own merits. We will be covering systems of linear equations, matrices and vectors, invertability, determinants, eigenvectors, diagonalization, ~~LU-decomposition~~ and the matrix exponential.

Do note that we will not be covering the topics rigorously in the lectures, but for the interested student the notes should contain a bit more information and the references given at the bottom of the page can be worth checking out.

## Lecturer

- Name: Endre Rundsveen
- Office: Sentralbygg 2, 8th. floor, room 832

## Tentative plan

Do note that this is only a tentative plan and can be changed before or during the course. If we collectively find that we can skip past some parts we may do that, or if we spend more time than planned on some part we may postpone the following parts.

Here are the notes from 2021.

Here are the notes for this year.

Day | Topic | Exercises | Notes + Recording | Notes from TMA4110/15 Only in Norwegian |
---|---|---|---|---|

Monday 8/8 | Short intro to ODEs | Exercises-1 + Solutions | Notes-1 Rec: Lecture 1 Rec: Lecture 2 | |

1st order ODEs | ||||

Integrating factor | ||||

Separable ODEs | ||||

Tuesday 9/8 | 2nd order ODEs | Exercises-2 + Solutions | Notes-2 Rec: Lecture 1 Rec: Lecture 2 | |

Homogeneous | ||||

Inhomogeneous | ||||

Wedenesday 10/8 | Numerical solutions | Notes-3 Rec:Lecture 1 Lecture 2 used for exercises | ||

Eulers method | ||||

Thursday 11/8 | Linear algebra | Exercises-4 + Solutions | Notes-4 Rec:Lecture 1 Rec:Lecture 2 | |

Systems of linear equations, Gaussian elimination | Lineære likninger | |||

Matrix operations | Matriser | |||

Matrix equations | Vektorlikninger | |||

Friday 12/8 | Linear independece | Exercises-5 + Solutions | Notes-5 Rec:Lecture1 Rec:Lecture2 | Lineær uavhengighet |

Subspaces | Vektorrom | |||

The determinant | Determinant | |||

Tuesday 16/8 | Eigenvectors | Exercises-6 + Solutions | Notes-6 | Egenvektorer |

Diagonalization | Diagonalisering | |||

Wednesday 17/8 | System of 1st order ODEs | Exercises-7 +Solutions | Notes-7 | Systemer av difflikninger Andre ordens difflikninger |

Matrix exponential | ||||

From nth order ODE to system | ||||

Thursday 18/8 | Phase portraits | No new exercises. | Notes contained in above notes. | |

Friday 19/8 | No lecture, but possibility of solving previous exercises with help. |

## Resources

You will not need any book to follow this course. The following resources can be used as supplementary sources, or any books you have used earlier for courses on linear algebra and differential equations. Do note that the listed books do cover a lot more than what we will be able to in our short course.

- Erwin Kreyszig

Advanced Engineering Mathematics

10th edition

ISBN 0-470-45836-4

- Introduction to Linear Algebra, fifth edition

Author: Gilbert Strang

ISBN: 978-0-9802327-7-6

- Differential Equations, Linear Algebra and its Applications, first/second edition

Compiled by: Institutt for matematiske fag, NTNU

ISBN: 978-1-78448-020-2

- Ordinary Differential Equations: Basics and Beyond

Authors: David G. Schaeffer, John W. Cain

ISBN: 978-1-4939-6387-4

DOI: https://doi.org/10.1007/978-1-4939-6389-8

- Matematikk i praksis

Authors: Tor Gulliksen, Amir M. Hashemi, Arne Hole

ISBN: 978-82-15-0208707

Note: Only in Norwegian

- Notes from TMA4110/15 - Mathematics 3

URL: https://wiki.math.ntnu.no/tma4115/2022v/fagstoff

Note: Only in Norwegian

- Helleviks kompendium i numerisk løsning av differensiallikninger