# TMA4165 Differential Equations and Dynamical Systems - Spring 2016

### Messages

- Takk for et hyggelig semester og god sommer!
**Exam (3.6.2016):**The exam and solutions can be found on the previous exams page!**Exam:****Final curriculum:**See lecture plan / topics page.- Fractals and chaos is
**not**part of the curriculum this year!

**Learning outcomes:**here**Support material code D:**- No printed or hand-written support material is allowed. A specific basic calculator is allowed.

- Lecture 26.4:
- Main topic: repetition and answering questions.
**It is up to you to ask questions or propose exam problems we should look at!**

- Lectures 19. and 21.4: I am going to plot some phase diagrams when talking about bifurcations and to repeat at the same time how to draw them.
- No exercise class: 19.4
- Next reference group meeting: 8.4
- There has been a crucial typo in the notes by Harald on the Poincare-Bendixson theorem. Follow the link below to download the corrected version!
- Exercise set 10: There has been a typo in the exercises that are going to be presented. You find a new version on the homework page!
- Updated the tentative curriculum on the lecture page!
- Here are the lecture notes from Week 11. They are not as detailed as the presentation in the class. There might also be some small mistakes. We are going to start in the middle of page 7 after easter.
- No lecture and no exercise class: 29.3
- No exercise class: 15.3
- Added a tentative curriculum on the lecture plan page!
- The course description and the learning outcomes can be found here.
- 1. Exercise class: Tuesday 19.1
- 1. lecture: Tuesday 12.1.
- Welcome to TMA4165 Differential Equations and Dynamical Systems!

### General information

The study of differential equations is a wide field in pure and applied mathematics, physics, and engineering. All of these disciplines are concerned with the properties of differential equations of various types. Pure mathematics focuses on the existence and uniqueness of solutions, while applied mathematics emphasizes the rigorous justification of the methods for approximating solutions. Differential equations play an important role in modelling virtually every physical, technical, or biological process, from celestial motion, to bridge design, to interactions between neurons. Differential equations such as those used to solve real-life problems may not necessarily be directly solvable, i.e. do not have closed form solutions. Instead, solutions can be approximated using numerical methods.

In pure mathematics, differential equations are studied from several different perspectives, mostly concerned with their solutionsâ€”the set of functions that satisfy the equation. Only the simplest differential equations are solvable by explicit formulas; however, some properties of solutions of a given differential equation may be determined without finding their exact form. If a self-contained formula for the solution is not available, the solution may be numerically approximated using computers. The theory of dynamical systems puts emphasis on qualitative analysis of systems described by differential equations, while many numerical methods have been developed to determine solutions with a given degree of accuracy.

- Wikipedia (2015), read the full article here.

### Lecturer

- Office 1138, Sentralbygg 2
- Office hours: Thursday 13:00-14:00

### Lectures

- Tuesday 08:15-10:00 F6
- Thursday 08:15-10:00 EL2

### Exercise assistant

- Fredrik Arbo HĂ¸eg

### Exercises

- Tuesday 16:15-17:00 K5
- A problem set will be given each week. They are part of the curriculum, but are not required to be handed in.

### Books and reading material

**Main book:**D.W. Jordan & P. Smith:*Nonlinear Ordinary Differential Equations: An Introduction to for Scientists and Engineers.*Fourth edition, Oxford University Press 2007.**Note:**H. Hanche-Olsen: Assorted notes on dynamical systems

### Reference group

- If you have any remarks, request, complaints etc. regarding this course, contact the lecturer or the reference group.

### Exam

- Dato: 3.6.2016
- Support material code D: No printed or hand-written support material is allowed. A specific basic calculator is allowed.