Computational Applied Mathematics
| Code | School | Level | Credits | Semesters |
| MATH4064 | Mathematical Sciences | 4 | 20 | Spring UK |
- Code
- MATH4064
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Spring UK
Summary
Four major topics for the computational solution of problems in applied mathematics are considered in this course:
- Approximation theory;
- numerical solution of nonlinear problems;
- numerical solution of ODEs;
- numerical solution of PDEs.
The focus is on formulating and understanding computational techniques with illustrations on elementary models from a variety of scientific applications. Specific contents include:
- Approximation theory, multivariate polynomial approximation, Gauss quadrature, splines, trigonometric polynomials, DFTs, FFTs;
- Numerical solution of (systems of) nonlinear equations;
- Numerical differentiation and numerical solution of ODEs;
- Introduction to PDEs, finite difference methods including error analysis.
Target Students
MSc Financial and Computational Mathematics in the School of Mathematical Sciences; Also available to Year 4 MMath, Natural Sciences and other MSc students.
Classes
- One 1-hour workshop each week for 10 weeks
- One 2-hour lecture each week for 10 weeks
- One 1-hour computing each week for 10 weeks
Assessment
- 20% Coursework 1: Assessed coursework including a computing component
- 20% Coursework 2: Assessed coursework including a computing component
- 60% Exam 1 (3-hour): Written examination.
Assessed by end of spring semester
Educational Aims
Thiscourse introduces computational methods for solving problems in applied mathematics. Students taking thiscourse will develop knowledge and understanding to design, justify and implement relevant computational techniques and methodologies.Learning Outcomes
A student who completes this course successfully should be able to:
L1 - Formulate and analyse polynomial approximations;
L2 - Formulate and analyse computational methods for the solution of nonlinear equations;
L3 - Formulate and analyse relevant numerical methods for ODEs and PDEs;
L4 - Implement computational algorithms using a sophisticated programming language.