Upon successful completion of the course, the student will be able to
Model simple processes and explain the basics of mathematical modelling
Formulate simple differential equations of first and second order
Draw and interpret direction fields and solution curves for differential equations and solve common types of linear, separable, and exact equations analytically
Determine stability properties of solutions of autonomous nonlinear differential equations
Use computers to find and present solutions and explore solution spaces
Explain some classical models where differential equations are used, and how the discipline of differential equations evolved historically
Contents
Introduction to mathematicel modelling. Analytical solution techniques for some common types of differential equations. Existence and uniqueness theorems for differential equations. Qualitative discussion of systems of autonomous differential equations. Use of computers to find and present solutions of differential equations and explore solution spaces. The students will encounter problems from economics, mechanics and ecology, which lead to difference and differential equations, and systems of such equations.
Teaching and learning methods
Lectures, group work, and mandatory hand-ins. Estimated workload of the course is 267 hours.
Examination requirements
Mandatory hand-ins must be approved. See Canvas for details.
Examinations
Written, supervised, and graded exam, 5 hours.
Student evaluation
The faculty member in charge of the module confers with the student rep which form of evaluation will be organized, and whether midterm or post hoc. Cfr the University regulations on quality assurance, chapter 4.1.