Ordinary differential equations 1 

• 14 hrs lecture
• 14 hrs problem session

The student is familiar with

1. elementary methods for solving ordinary differential equations (separating variables, exact equations).
   
2. the most important theorems concerning existence and uniqueness of soluitions.
   
3. the reduction of equations of higher order to systems of equations of order one.
4. the theory of linear differential equations, in particular equations with constant coefficients.
5. Furthermore, he can solve differential equations in terms of power expansions.
   

Ordinary differential equations (ODEs) are equations where a function y(x), which is being sought, appears together with finitely many of its derivatives. (The simplest case is y'(x)=f(x,y(x)), where f is a given continuous function.) Almost all dynamical systems arising in mechanics, engineering, biology, economy can be discribed in terms of ODEs. Of course, ODEs also play an important role in pure mathematics, for example in differential toplogy, and also as point of departure for the theory of partial differential equations. Part 1 of this course will give an introduction to the theory of ODEs, focussing on the structure of the solutions and concrete computational methods. This course can be folowed without knowledge of Analysis 2 and 3 and therefore is suitable also for students of physics.