# Unit information: Ordinary Differential Equations 2 in 2016/17

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Unit name Ordinary Differential Equations 2 MATH20101 20 I/5 Teaching Block 1 (weeks 1 - 12) Professor. Wiggins Not open MATH 11007 Calculus 1 and MATH 11005 Linear Algebra & Geometry; Calculus 2 recommended but not required. None School of Mathematics Faculty of Science

## Description including Unit Aims

Unit aims

The aim of this unit is to introduce the students to the basic theory of ordinary differential equations and give a competence in solving ordinary differential equations by using analytical or numerical methods.

General Description of the Unit

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 interpretate the solutions of these equations. This unit explains different methods of solution of ordinary differential equations: from analytical to numerical.

Relation to Other Units

This unit develops the ordinary differential equations material in Core Mathematics. Partial differential equations are treated in a separate unit, Applied Differential Equations 2. Together with Calculus 2, these courses provide essential tools for mathematical methods and applied mathematics units at Levels 3 and 4. Calculus 2 is recommended but not required as a corequisite.

## Intended Learning Outcomes

Learning Objectives

The student will learn to formulate ordinary differential equations (ODEs) and seek understanding of their solutions, either obtained exactly or approximately by analytic or numerical methods. Students should understand the concept of a solution to an initial value problem, and the guarantee of its existence and uniqueness under specific conditions. The student will recognize basic types of differential equations which are solvable, and will understand the features of linear equations in particular. Students will learn to use different approaches to investigate equations which are not easily solvable. In particular, the student will be familiar with phase plane analysis. Students will become proficient with the notions of linearization, equilibrium, stability. They will learn to use the eigenvalue method for autonomous systems on the plane.

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

100% Examination.

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.