## MAS340 Mathematics (Computational Methods)

Note: Information for future academic years is provisional. Timetable information and teaching staff are especially likely to change, but other details may also be altered, some courses may not run at all, and other courses may be added.

 Semester 2, 2019/20 10 Credits Lecturer: Dr Julia Rees Timetable Reading List Aims Outcomes Assessment

Prerequisites: MAS254 (Computational and Numerical Methods)
No other modules have this module as a prerequisite.

## Outline syllabus

• Numerical methods
• A brief review of MATLAB (variables, matrices, solving linear equations);
• Numerical solutions of partial differential equations (Taylor series, parabolic equations, implicit method, Crank-Nicolson method, elliptic equations);
• Cubic splines.
• Optimization
• Functions of two variables;
• Descent methods for functions of several variables;
• Newton's method;
• Integer programming;
• Dynamic programming.

## Aims

• To prepare the numerical background for solving partial differential equations arising in engineering applications.
• To introduce the use of MATLAB package for solving mathematical equations.
• To introduce the elements of the powerful mathematical programming tools through simple examples and problems of small dimension.
• To give a geometric interpretation of unconstrained optimization using the idea of descent directions.
• To study Integer Programming (IP) logic modelling.
• To introduce the concepts of Dynamic Programming (DP).

## Learning outcomes

• To be able to recognise and implement finite difference approximations
• To be able to solve a variety of differential equations describing real problems
• To be able to use mathematical packages (MATLAB) to solve problems and to visualize the results
• To be able to solve simple optimisation problems using descent methods for unconstrained problems and IP methods for constrained problems
• To be able to use the Dynamic Programming methodology in simple applications

19 lectures, no tutorials

## Assessment

One 2 hour examination (85%). Project work (15%).