Overview
MATH2121 is a Mathematics Level II course.聽
Units of credit:听6
Prerequisites:聽MATH1231 or MATH1241 or MATH1251 or DPST1014
Exclusions:聽MATH2018, MATH2019, MATH2221.
Cycle of offering:聽Term 2聽
Graduate attributes:聽The course will enhance your research, inquiry and analytical thinking abilities.
More information:聽The course outline contains information about course objectives, assessment, course materials and the syllabus.
Important additional information as of 2023
国产精品 Plagiarism Policy
The University requires all students to be aware of its聽.
For courses convened by the聽School of Mathematics and Statistics no assistance using generative AI software is allowed unless specifically referred to in the individual assessment tasks.
If its use is detected in the no assistance case, it will be regarded as serious academic misconduct and subject to the standard penalties, which may include 00FL, suspension and exclusion.
罢丑别听聽contains up-to-date timetabling information.
The higher version of this course,聽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聽聽this course.
Course aims
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 cannon balls. DEs now have applications in fields as diverse as biology (spread of epidemics), medicine (growth of tumours), sociology (emigration rates), psychology (learning theories), economics (option pricing), chemistry (reaction rates), physics (dynamics of a laser) and engineering (electric circuits). Exact and numerical methods for solving DEs are therefore of fundamental importance for understanding nature and technology.
In first year, we 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 apply a dynamical systems approach to systems of ordinary differential equations and give an introduction to solving ordinary differential equations numerically. We learn how to find solutions of differential equations that obey prescribed boundary conditions. Not all differential equations can be solved in terms of "elementary" functions such as polynomials, exponentials or trigonometric functions. 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.
Course description
The following topics are treated both theoretically and with illustrative applications in physics, engineering and biology.
Ordinary differential equations: first order, linear second order, variation of parameters, dynamical systems, power series representations and Frobenius method, orthogonal functions and Fourier series, initial and boundary value problems, eigenfunction expansions, Bessel's equation.
Partial differential equations: classification, method of separation of variables, application of Fourier series, heat equation, wave equation, Laplace's equation, applications of Bessel functions.