# MATH2121 Theory and Applications of Differential Equations

MATH2121 is a Mathematics Level II course. See the course overview below.

This course was previously MATH2120 a 3uoc course which is no longer offered.

Units of credit: 6

Prerequisites: MATH1231 or Math1241 or MATH1251.

Exclusions: MATH2019, MATH2029, MATH2059, MATH2221.

Cycle of offering: Term 2

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

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

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

The higher version of this course, MATH2221 Higher Theory and Applications of Differential Equations, is also offered yearly in Semester 2.

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

If you are currently enrolled in MATH2121, you can log into UNSW Moodle this course.

#### Course Overview

Differential Equations (DEs) were first introduced by Newton to describe the behaviour of dynamical systems such as the motions of the planets and the trajectories of canon balls. DEs now have applications in biology (spread of epidemics), medicine (growth of tumours), sociology (emigration rates), psychology (learning theories), economics (option pricing), chemistry (reaction rates), physics (flight of a cricket ball) and engineering (electric circuits). Methods for solving DEs are therefore of fundamental importance for understanding nature and technology. In first year you learnt how to solve first-order ordinary differential equations and second-order ordinary differential equations with constant coefficients.

In MATH2121 we learn how to deal with second-order ordinary differential equations with variable coefficients and with 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 using Sturm-Liouville methods and Fourier series methods.