Content:

1. Introduction to mathematical modelling with differential equations: Modelling cycle, principles and observations, types of problems, scaling and dimensional analysis, simplification and reduction, perturbation methods.
2. Intro to differential equations: Classification, general first order equations, autonomous equations, stability, integrating factors for linear equations, separation and substitution methods for nonlinear equations.
3. Systems and higher order equations: Relation between higher order equations as systems, general 2x2 systems, autonomous systems, phase portraits, linearisation and linear stability, general theory for linear systems, eigenspace analysis in case of constant coefficients.
4. Further problems and techniques: a selection from discretisation principles and difference equations, control problems, dynamical systems, attractors and linearisation.

Books:

Robinson, James C. An Introduction to Ordinary Differential Equations. Cambridge University Press, 2004.

Witelski, B. and Bowen, M., Methods of Mathematical Modelling: Continuous Systems and Differential Equations. Springer, 2015.

Logan, David. A First Course in Differential Equations. Springer, 2015.

Holmes, Mark H. Introduction to the Foundations of Applied Mathematics. Springer, 2019.