 # MATH2221 Higher Theory and Applications of Differential Equations

MATH2221 is a Mathematics Level II course; it is the higher version of MATH2121 Theory and Applications of Differential Equations. See the course overview below.

This course has replaced MATH2130 and is now a 6uoc course

Units of credit: 6

Prerequisites: MATH1231 or Math1241 or MATH1251, each with a mark of 70 or higher.

Exclusions: MATH2019, MATH2029, MATH2059, MATH2121.

Cycle of offering: Term 2

Graduate attributes: The course will enhance your research, inquiry and analytical thinking abilities.

More information: This recent course handout (pdf) contains information about course objectives, assessment, course materials and the syllabus.

The Online Handbook entry contains up-to-date timetabling information.

MATH2221 (alternatively MATH2121) is a compulsory course for Mathematics majors.

If you are currently enrolled in MATH2221, you can log into UNSW Moodle for this course.

#### Course Aims

This course aims to build on your previous study of ordinary differential equations (ODEs) as part of first year calculus. We begin by studying initial-value problems for second and higher-order linear ODEs. Next is an overview of first-order systems of ODEs, touching on a range of topics that are treated at greater depth in our third-year courses. We then return to the topic of linear second-order ODEs, but consider boundary-value problems, as well as a first look at separation of variables for partial differential equations (PDEs). The remainder of the course treats eigenproblems for ordinary and partial differential operators, and their use for solving initial boundary-value problems for PDEs using Cartesian or polar coordinates.

Although the main focus of the course is on analytical methods of solution, we also discuss a variety of applications that give rise to differential equation models.

#### Course Description

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.