Upon successful completion of the course, the student will be able to
model simple processes and explain the main steps in mathematical modeling
explain some classical models where differential equations are used
draw and interpret direction fields and solution curves of differential equations
decide conditions for existence and uniqueness of solutions
set up and solve first order difference equations
set up and solve systems of linear differential equations
solve some classes of nonlinear ordinary differential equations
interpret systems of nonlinear autonomous differential equations qualitatively
Course contents
Introduction to and awareness of the steps in a mathematical modeling process, including analytical solutions of some common differential equations ( first and second order linear differential equations, separable, homogeneous and exact equations, linear systems of equations with constant coefficients). Introduction to the theory of existence and uniqueness of solutions, and to the qualitative study of autonomous equations. The student will meet problems from economics, mechanics and ecology which lead to first and second order differential equations, and systems of first order differential equations (i.a. population dynamics).
Teaching methods
Lectures, work in small groups and compulsory assignemets. The course has an expected workload of around 200 hours.
Examination requirements
Required assignments must be approved, see Canvas for more information.
Assessment methods and criteria
5-hour written examination. Graded assessment.
Evaluation
The person responsible for the course, in consultation with the student representative, decides the method of evaluation and whether the courses will have a midterm- or end of term evaluation, see also the Quality System, section 4.1. Information about evaluation method for the course will be posted on Canvas.