This course aims to give students an understanding of linear differential equations (both ordinary and partial) including the construction of their solutions by a variety of techniques.

34 x 1hr lectures and 12 x 1hr tutorials in a semester.

Mathematical Methods I (86PP)
Mathematical Methods II (86PQ)

90% Examination, 10% Coursework.

The course Mathematical Methods aims to give a comprehensive treatment of techniques for the solution of linear ordinary differential equations, including eigenvalue problems, and commonly occurring partial differential equations given initial and boundary conditions that are appropriate for each type of equation. The techniques to be covered include series solutions, Green's function methods, the method of separation of variables, and the method of characteristics.

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

■ classify differential equations according to order, degree and linearity;

■ construct exact solutions to second order linear differential equations by a variety of techniques, including Wronskians and integrating factors;

■ construct series solutions for second order ordinary differential equations about ordinary and regular singular points;

■ construct Green's functions and handle delta functions for simple systems of equations;

■ solve simple eigenvalue/boundary value problems;

■ establish the orthogonality of eigenfunctions and use this property to construct an eigenfunction expansion.

■ solve a first order linear or quasilinear partial differential equation;

■ determine the regions of the xy-plane in which the general second order partial differential equation in two dimensions is hyperbolic, parabolic or elliptic and subsequently reduce the equation to its canonical form and determine the characteristic equations;

■ solve partial differential equations by the method of separation of variables for given initial and/or boundary conditions.