MTH5321 - Methods of computational mathematics - 2019

Computational methods are of paramount importance for solving real-world problems in applied mathematics.This unit teaches widely used numerical methods for problems from science, engineering, biology and finance that are modeled by partial differential equations (PDEs). The unit covers numerical methods for PDEs of elliptic, parabolic and hyperbolic type, as well as advanced solution methods for the linear and nonlinear systems of equations that may arise from the discretisation of the PDEs. Topics covered may include finite difference methods, finite element methods, and finite volume methods; iterative and multigrid solvers for linear and nonlinear systems; nonlinear hyperbolic conservation laws; and other topics in numerical PDEs.The concepts of numerical accuracy, stability and efficiency play a central role in the unit. Students will receive an introduction to the theory of the numerical methods (with derivations of the methods and some proofs), and will learn to implement the computational methods efficiently. Applications will be covered from various domains such as heat transfer, option pricing, biology, and fluid mechanics.

On completion of this unit students will be able to:

1. Explain the mathematical theory behind a selection of important numerical methods for PDEs, including the derivation of the methods and the analysis of their properties.
2. Explain and apply notions of accuracy, stability and computational cost when solving PDE problems numerically.
3. Demonstrate proficiency in numerical methods for PDEs and linear system solving, and apply them to problems in science, engineering, biology and finance.
4. Implement advanced numerical PDE methods, and demonstrate the correctness and efficiency of the implementations in systematic computational tests.
5. Apply critical thinking and demonstrate written and oral communication skills in the field of computational mathematics.

Examination (3 hours): 60% (Hurdle)

Continuous assessment: 40%

Hurdle requirement: To pass this unit a student must achieve at least 50% overall and at least 40% for the end-of-semester exam.

This unit is offered at both Level 4 and Level 5, differentiated by the level of the assessment. Students enrolled in MTH5321 will be expected to demonstrate a higher level of learning in this subject than those enrolled in MTH4321. The assignments and exam in this unit will use some common items from the MTH4321 assessment tasks, in combination with several higher level questions and tasks.

3 hours of lectures and 1 hour of tutorial per week

10 hours of independent study per week

See also Unit timetable information

Master of Mathematics