## MAS340 Mathematics (Computational Methods)

Note: This is an old module occurrence.

You may wish to visit the module list for information on current teaching.

 Semester 2, 2019/20 10 Credits Lecturer: Dr Julia Rees 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%).