MAS340 Mathematics (Computational Methods)
|Semester 2, 2022/23||10 Credits|
|Lecturer:||Dr Julia Rees||Reading List|
Prerequisites: MAS254 (Computational and Numerical Methods)
No other modules have this module as a prerequisite.
- 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.
- Functions of two variables;
- Descent methods for functions of several variables;
- Newton's method;
- Integer programming;
- Dynamic programming.
- 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).
- 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
One 2 hour examination (85%). Project work (15%).
|B||Atkinson and Han||Elementary Numerical Analysis||Blackwells||Amazon|
|B||Kreyszig||Advanced Engineering Mathematics||Blackwells||Amazon|
(A = essential, B = recommended, C = background.)
Most books on reading lists should also be available from the Blackwells shop at Jessop West.