O R D I N A R Y    D I F F E R E N T I A L   E Q U A T I O N S 

Good luck in the exam!

OVERVIEW

This page will be used to make announcements and provide copies of handouts, lecture notes, problem sheets and their solutions for this course. Files will be supplied in pdf format.

I welcome feedback in the form of constructive comments or criticism. Just send an email to or talk to me after the lectures. My office hours are Mondays at 1pm and Tuesdays at 10am.

Information handout

LECTURE NOTES

Lecture notes are available at MyCavehill eLearning.

Note: Lecture notes are not a textbook! There might be misprints as well as mathematical errors (please do notify me, preferrably by email, if you spot an error, even if it is only a minor misprint).

EXERCISE SHEETS

Exercise sheet 12 with solutions (without solutions)

Exercise sheet 11 with solutions (without solutions)

Exercise sheet 10 with solutions (without solutions)

Exercise sheet 9 with solutions (without solutions)

Exercise sheet 8 with solutions (without solutions)

Exercise sheet 7 with solutions (without solutions)

Exercise sheet 6 with solutions (without solutions)

Exercise sheet 5 with solutions (without solutions)

Exercise sheet 4 with solutions (without solutions)

Exercise sheet 3 with solutions (without solutions)

Exercise sheet 2 with solutions (without solutions)

Exercise sheet 1 with solutions (without solutions)

SELF-ASSESSMENT SHEETS

Self-assessment sheet 3

Self-assessment sheet 2

Self-assessment sheet 1

PROJECT DESCRIPTIONS

For details how to do the projects, see MyCavehill eLearning.

Compensating a sudden change in demand

Electrical circuits

Fishery and harvesting

Mixing problems

Oceanography: Layers of different concentration profiles

Population models

Pursuit curves

Mechanical vibrations

CLASS TEST

Midsemester test (including sketch of solutions)

ADDITIONAL MATERIALS

Wikipedia on "Convolution": Watch the animations on the right hand side.

The applet "Contour diagram Grapher/3D Grapher" graphs user-defined 3D views and the level sets of potential functions.

The applet "Implicit Equations Grapher" graphs user-defined implicit equations, i.e., a single level set.

More on numerical methods how to obtain (numerical) solutions of ODEs can be found in the "Numerical Recipes" books by W.H. Press et al.; see Chapter 16 of "Numerical Recipes in C" or "Numerical Recipes in Fortran 90" which start with Euler's method.

YouTube video "Physics: magnetic field of a magnet": Iron fillings make magnetic field lines visible.

Wikipedia on "The SIR model" for infectious diseases.

Wikipedia on "Pendulum": Read the section "Period of oscillation"; also see the wikipedia article on "Pendulum (mathematics)".

DIARY

14.4.: solving differential equations using Laplace transform; convolution

12.4.: properties of Laplace transform

7.4.: Picard-Lindelöf for higher order linear differential equations; Wronskians; introduction to Laplace transforms

31.3.: Picard iteration; Power series

29.3.: Volterra equation; Picard-Lindelöf theorem

24.3.: Cauchy sequences; Banach's Contraction Mapping Principle; Lipschitz continuous functions

22.3.: boundary values; reduction of order; metric spaces

17.3.: inhomogeneous linear differential equation with constant coefficients

15.3.: homogeneous linear differential equation with constant coefficients

10.3.: existence & uniqueness of solutions of a linear differential equation; homogeneous linear differential equation with constant coefficients

3.3.: complex numbers and complex functions; linear independence and Wronskian

1.3.: variation of parameters; introduction to linear differential equations of order greater than one

24.2.: proof of criterion for exactness of a differential equations; linear differential equations of first order

22.2.: integrating factors

17.2.: further substitution methods; exact differential equations

15.2.: further substitution methods

10.2.: existence & uniqueness of solutions of separable differential equations; homogeneous differential equations

8.2.: separable differential equations

3.2.: construction of a direction field; ordinary & singular points; intro separable differential equations

1.2.: initial conditions & initial value problem; direction field

27.1.: definition of differential equation; general & particular solution

25.1.: introduction & overview