MATH3700Partial Differential Equations

Course handbook

Description

Partial differential equations arise from the mathematical modelling of a wide range of problems in biology, engineering, physical sciences, economics and finance. Therefore, they form an essential part of the mathematical background required for engineering and physical sciences. This course introduces students to the modern theory and methods of partial differential equations. It provides the students with the skills to formulate partial differential equations using conservation laws and the knowledge of solving them using some fundamental analytical and numerical methods.

Availability2020 Course Timetables

Learning outcomes

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

1. Build mathematical models of relevant real-world problems based on partial differential equations in studying differential equations.

2. Classify second order partial differential equations, apply analytical methods to solve them, and physically interpret the solutions.

3. Apply numerical methods to solve practical partial differential equations and implement them in computers.

4. Analyse the consistency, stability and convergence properties of numerical methods.

5. Use qualitative analysis and notion of weak solutions of important classes of partial differential equations to investigate properties of their solutions.

Content

• Modelling with partial differential equations. 
• Classical solution techniques: method of characteristics, separation of variables and Fourier series, fundamental solution and Green’s function, transform method.
• Qualitative analysis and weak solution: maximum and minimum principles, well-posedness, weak solution.
• Numerical methods for partial differential equations: consistency, stability and convergence.

Assumed knowledge

MATH2800

Assessment items

Quiz: Quiz

Written Assignment: Assignments

Formal Examination: End of Semester Exam

Contact hours

Callaghan