# TMA4165 Differential Equations and Dynamical Systems - Spring 2017

### Messages

- Takk for et hyggelig semester og god sommer!
**Exam (23.5):**- The exam and solutions can be found on the previous exams page!
- The solutions present one way to solve the exam problems! If your solution differs it might still be ok!
- Corrected a mistake in the solution to exercise 2b!

**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.

**Mattelab**:- 16.5: 14:00-17:00 (S23/S24)
- 19.5: 14:00-17:00 (S23/S24)

- 2. Reference group meeting: 13.3
- Added a book for further reading in the list below. This book is
**not**part of the curriculum. - 1. Reference group meeting: 30.1.
- The lectures on Thursday are moved from B1 to R2.
- The course description and the learning outcomes can be found here.
- 1. Exercise class: 16.1.2017
- 1. lecture: 9.1.2017
- 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 solutions—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 (2016), read the full article here.

### Lecturer

- Office 1138, Sentralbygg 2

- Office 1254, Sentralbygg 2

### Lectures

- Monday 12:15-14:00 S1
- Thursday 12:15-14:00
**R2**

except

- Thursday 26.1.: S1
- Thursday 2.2.: B1
- Thursday 9.2.: F2
- Thursday 9.3.: G1

### Exercises

- Monday 14:15-15:00 F6
- 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**Note:**K. Grunert: Traveling wave solutions for the Korteweg-de Vries equation

**Further reading:**

- G. Teschl:
*Ordinary Differential Equations and Dynamical Systems.*Graduate Studies in Mathematics, Volume 140, Amer. Math. Soc., Providence, 2012. (Covers e.g. matrix exponentials and Hartman-Grobman in detail.)

### Reference group

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

### Exam

- Dato: 23.5.2017
- Support material code D: No printed or hand-written support material is allowed. A specific basic calculator is allowed.