MAT7106 Partial Differential Equations

This course will discuss partial differential equations (PDEs), emphasizing the wave, diffusion and potential (Laplace) equations. The focus will be on understanding the physical meaning and mathematical properties of solutions of partial differential equations. Methods we will use include fundamental solutions and transform methods for problems on the line, and separation of variables using orthogonal series for problems in regions with boundary. The course will also emphasize numerical techniques for solving partial differential equations. Particular emphasis will be a blend of theory and numerical applications, however, rather than simply present one scheme after another, the goal is to dig deeper and understand why some schemes work and others don't.
Parabolic PDEs, numerical solution of elliptic PDEs and finite element method will be emphasized.

Course Objectives
The main objectives of this course are:

• To provide the fundamental base for the “Numerical Solution of Partial Differential Equations.
• Developing of applications of Numerical techniques in partial differential equations.
• Providing the base for research in partial differential equations.

Learning Outcomes
After completing the course, the student is expected to:

• Solve different applied problems in engineering and science.
• Use this course in Marine engineering, fluid dynamics, hydrodynamics and fluid flow