MATH3700Advanced Differential Equations

Course handbook

Description

This course introduces students to the modern theory and methods of ordinary and partial differential equations. It builds on the classical foundations of differential equations studied in second year. Ordinary and partial differential equations form an essential part of the mathematical background required for engineering and the physical sciences. A large number of real-life problems can be modelled using differential equations, making the subject one of the most widely applicable areas of mathematics. The course concentrates on some fundamental analytical and numerical methods for applied differential equations arising from the mathematical modelling of physical, chemical and biological systems.

Availability

Learning outcomes

On successful completion of the course students will be able to:

1. Have a broad overview of ordinary and partial differential equations as well as an appreciation of the application of analysis and linear algebra in studying differential equations.

2. Have the skills to build mathematical models of relevant real-world problems based on differential equations.

3. Be able to solve these differential equations using appropriate computer software if necessary, and to interpret the solutions.

4. Understand the concepts of accuracy, consistency, stability and convergence of numerical schemes for solving differential equations.

Content

(1) Ordinary Differential Equations

• (a) Existence and uniqueness theory for ordinary differential equations
• (b) Stability theory for linear and nonlinear ordinary differential equations
• (c) Stability and convergence of numerical techniques, and numerical schemes for stiff ordinary differential equations

(2) Partial Differential Equations

• (a) Modelling with partial differential equations
• (b) Classical solution techniques and weak solutions
• (c) Numerical methods for partial differential equations

Assumed knowledge

MATH2800 and MATH2320 or MATH2470 and MATH2320

Assessment items

Quiz: Quiz

Written Assignment: Assignments

Formal Examination: End of Semester Exam

Contact hours

Callaghan