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, 2018/19 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%).

Reading list

Type Author(s) Title Library Blackwells Amazon
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.