Handbook

• In first year you learnt how to solve first order ordinary differential equations and second order ordinary differential equations with constant coefficients. In this course we learn how to deal with second order ordinary differential equations with variable coefficients and give an introduction to partial differential equations. We also learn how to find solutions that obey prescribed boundary conditions. Not all DEs can be solved in terms of known functions such as polynomials, exponentials and the like. A major aim of this course is to teach you how to get information about the solution in these cases using power series methods and Frobenius' method. A second major aim is to learn how to find solutions to boundary value problems in 1D using Sturm-Liouville methods and Fourier series methods, and to learn how to find solutions to boundary value problems in 2D using Elliptic differential operators, Green identities, Elliptic eigenproblems and Wave and diffusion equations.

• This course is a prerequisite for the third year courses MATH3121 Mathematical Methods and Partial Differential Equations, MATH3120 Dynamical Systems and Chaos, and MATH3261 Fluids, Oceans and Climates.

As for MATH2121, but in greater depth, and with some additional topics.