Unit Code: MTH806

Unit Name: Advanced Ordinary Differential Equations

Description: Ordinary differential equations (ODE) are fundamental to the mathematical vocabulary used to describe natural phenomena. This course is designed to introduce students to advanced ordinary differential equations (ODEs) by providing the theory and methods of solving ODEs. Topics include the general theory of linear differential equations, the existence and uniqueness of solutions, initial value problems, Picard’s method, Strums separation and comparison theory on the qualitative properties of solutions, boundary value problems, Sturm–Liouville problems, Green’s functions, and power series method.

Learning Target Outcomes: As a result of successfully completing this course, the student will be able to: 1. Analyze the qualitative properties of systems of ordinary differential equations. 2. Solve linear ordinary differential equations using series methods and Green\'s functions. 3. Develop analytical skills to solve a wide range of ordinary differential equations. 4. Solve Sturm-Liouville eigenvalue problems. 5. Apply differential equations to model physical situations.

Prerequisite: Minimum Entry Requirements of the programme

Prerequisite Sentence: Minimum Entry Requirement of the programme

Credit Point: 30

Offered In: Semester 1,2