Unit information: Ordinary Differential Equations 2 in 2019/20

Description including Unit Aims

The aim of this unit is to introduce the students to the basic theory of ordinary differential equations.

Unit Description

The subject of differential equations is a very important branch of applied mathematics. Many phenomena from physics, biology and engineering may be described using ordinary differential equations. In order to understand the underlying processes we have to find and interpret the solutions of these equations; this unit is an introduction to the endeavour.

Relation to Other Units

This unit develops the ordinary differential equations material in ODEs, Curves and Dynamics. Partial differential equations are treated in a separate unit, Applied Partial Differential Equations 2. Together with Multivariable Calculus and Methods of Complex Functions, these courses provide essential tools for mathematical methods and applied mathematics units at Levels 3 and 4.

Intended Learning Outcomes

Learning Objectives

By the end of this unit students will be able to:

• recognize basic types of differential equations and understand the features of linear equations in particular.
• use phase plane analysis to investigate equations which are not easily solvable.
• apply the notions of equilibrium, linearization, stability and bifurcation to problems arising in physics, biology and engineering etc.

Transferable Skills

• Increased understanding of the relationship between mathematics and the “real world” (meaning the physical, biological, economic, etc. systems).
• Development of problem-solving and analytical skills.

Teaching Information

Lectures - 33 sessions in which the lecturer will present the course material on the blackboard. Students are expected to attend all lectures, and to prepare for them by reading notes, handouts or texts, as indicated by the lecturer. The lectures are 3 per week, on weeks 1 to 11 - no class on week 12 .

Problems classes - 10 sessions with the lecturer, in which problems will be worked through as a demonstration, on the blackboard. Students are strongly encouraged to attend all problems classes.

Homework assignments - 10 problem sheets will be given out, one per week. Students will be required to turn in selected problems from the sheet, which will be marked by the postgraduate teaching assistants.

Assessment Information

Reading and References

Recommended

• Stephen Wiggins, Ordinary Differential Equations, Independent, 2017