To consolidate and extend the understanding of mathematics required for the physical sciences. To develop the student’s ability to apply the mathematical techniques developed in the module to the understanding of physical problems.

(LO1) Familiarity with methods for solving first and second order differential equations in one variable.

(LO2) Familiarity with methods for solving partial differential equations with applications.

(LO3) A basic knowledge of integral vector calculus.

(LO4) A basic understanding of Fourier series and transforms.

(LO5) A basic understanding of series methods for the solution of differential equations.

(S1) Numeracy.

(S2) Problem solving skills.

(S3) Collaborative learning.

Differential equations.
First and second order differential equations in one variable, integrating factors, homogenous (and inhomogeneous) equations.

Integral vector calculus.
Line and surface integrals in cartesian and polar coordinate systems.

Partial Differential equations.
Characteristics and separation of variables with examples with examples with references to the wave equation, heat equation, Schrodinger equation, Poisson equation, Laplace equation etc.

Teaching Method 1 - Lecture
Description: 12 x 3 lectures/week
Attendance Recorded: Yes

Teaching Method 2 - Problems Class
Description: 12 x 2-hour problems classes. Students attempt a range of problems associated with the course material, under supervision of the lecturer and demonstrators
Attendance Recorded: Yes

Asynchronous learning materials (notes/videos/exercises etc) will be made available to students through the VLE. The module will have regular synchronous sessions in active learning mode.