# TMA4165 -- Differential Equations and Dynamical Systems Spring 2022

## General Info

### Messages

• 1st lecture: Monday 1/10 (online) Refer to Blackboard to get the access details to the Zoom meeting
• 1st exercise class: Tuesday 1/18 (online)

### 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 emphasises 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.

### Lecturer

• Office 1002, Sentralbygg 2
• Office hours: Friday, 17:00 - 18:00 (Please write me a message in advance)

### Exercises

• Typically a problem set will be given every second week. Exercises classes will be given every second week .
• A project will be given at some point of the semester.
• The problems sets will be supervised in the exercise class. They are part of the curriculum, but are not required to be handed in.
• In general the exercise class is the right place to
• get help with the problem sets (because solution sheets to all the problems will not be provided)
• discuss and ask questions about the material covered in the course