Unit information: Ordinary Differential Equations 2 in 2020/21

Unit name	Ordinary Differential Equations 2
Unit code	MATH20101
Credit points	20
Level of study	I/5
Teaching block(s)	Teaching Block 1 (weeks 1 - 12)
Unit director	Dr. McGillivray
Open unit status	Not open
Pre-requisites	MATH10012 ODEs, Curves and Dynamics and MATH11005 Linear Algebra and Geometry.
Co-requisites	Multivariable Calculus is recommended but not required as a co-requisite.
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

The aim of this unit is to introduce the basic theory of ordinary differential equations (ODEs).

Unit Description

Ordinary differential equations are very important in applied mathematics. Many phenomena from physics, biology and engineering may be described using ODEs. In order to understand the underlying processes we have to interpret the solutions of these equations; this unit is an introduction to the endeavour.

Syllabus

• What is a dynamical system?
• The geometric point of view. Flows in one and two dimensions.
• Stability and linearization. Invariant sets and manifolds.
• Elementary bifurcation theory.

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 ODEs 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

The unit will be taught through a combination of

• synchronous online and, if subsequently possible, face-to-face lectures
• asynchronous online materials, including narrated presentations and worked examples
• guided asynchronous independent activities such as problem sheets and/or other exercises
• synchronous weekly group problem/example classes, workshops and/or tutorials
• synchronous weekly group tutorials
• synchronous weekly office hours

Assessment Information

90% Examination 10% Coursework

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

If you fail this unit and are required to resit, reassessment is by a written examination in the August/September Resit and Supplementary exam period.

Reading and References

Recommended

• Stephen Wiggins, Ordinary Differential Equations, Independent, 2017