Wiki page, MVE162 / MMG511 Ordinary differential equations and mathematical modelling Spring 26: Lectures/Exercise sessions

Wiki page
2025-11-11T07:59:39+01:00

Lectures:

The lecture notes can be found here (they are work in progress, feel free to notify me if you find mistakes, errors or misprints).

However, for those of you who prefer the previous course book (denoted by LR from now):

Hartmut Logemann, Eugene P. Ryan
Ordinary Differential Equations Analysis, Qualitative Theory and Control Springer-Verlag London 2014

Springerlink to the book here.

The lectures follow the lecture notes quite closely and all exercises in the notes should be considered useful for understanding. Some of these exercises will also be discussed during the exercise sessions. All problems from last year's exams have been incorporated into the exercises in the notes.

Towards the end of the course, a model exam will be constructed.

Before easter break

Lecture 1 (23/3): Introduction and overview of the course. Some simple models and basic questions to be discussed during the course.

Lecture 2 (25/3): Existence and (non-)uniqueness of solutions of ODEs.

Lecture 3 (26/3): Dependence on initial conditions. Maximal intervals of definition.

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Lecture 4 (30/3): Linear differential equations and matrix exponentials.

Lecture 5 (1/4): Linear differential equations beyond matrix exponentials.

After easter break

Exercise session 1 (13/4): Explicit computations with exponentials and fundamental matrices. A little bit of Floquet theory.

Lecture 6 (15/4): Grönwall's lemma and Lipschitz dependence on initial values.

Lecture 7 (16/4): The notions of stability and asymptotic stability: linear cases.

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Exercise session 2 (20/4): Explicit examples around stability and asymptotic stability.

Lecture 8 (22/4): Stability of perturbations, linearisation (hyperbolic case).

Lecture 9 (23/4): Lyapunov functions ans stability/asymptotic stability, La Salle's criterion.

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Exercise session 3 (27/4): Examples with stability of perturbations and Lyapunov functions.

Lecture 10 (29/4): The flow box theorem and a crash course on metric spaces, completeness, Banach's fixed point theorem.

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Lecture 11 (4/5): Hartman-Grobman's Theorem

Exercise session 4 (6/5): Examples around local conjugacies

Lecture 12 (7/5): Bifurcations and centre manifolds

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Exercise session 5 (11/5): Limit cycles and Poincare-Bendixson

Lecture 13 (13/5): Important models I

(Kristi himmelsfärd)

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Lecture 14 (18/5): Important models II

Exercise session 6 (20/5): Crash course on variational calculus

Lecture 15 (21/5): Important models III

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Repetition I (25/5):

Repetition II (27/5):

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