Aims

To lay the mathematical foundations for more advanced mathematics needed to describe
physical systems. Students will learn how to solve simple differential equations and how known computational tools of the calculus of functions of a single variable generalize to functions of many variables.

Outline Of Syllabus

A general introduction to differential equations: Partial and ordinary; linear and non-linear; homogeneous and non- homogeneous. First-order ordinary differential equations (ODEs): direct integration; separation of variables, homogeneous equations, general linear first order ODEs. Second-order linear ODEs: Constant coefficients, inhomogeneous equations. Partial differentiation of multivariable functions: stationary points, chain rule. Integration of multivariable functions: Double and triple integration, change of variables, polar, spherical and cylindrical coordinates.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. The small group tutorials allow students to improve their understanding of fundamental material and to develop mathematical presentation skills. Office hours provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. One written assignment and one mid-semester class test allow the students to develop their problem solving techniques, to practise the methods learnt in the module and to receive feedback; this is thus formative as well as summative assessment.