MAS254 Computational and Numerical Methods

Note: This is an old module occurrence.

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

Semester 2, 2015/16 10 Credits
Lecturer: Dr Gary Verth Timetable Reading List
Aims Outcomes Teaching Methods Assessment

Prerequisites: MAS152 (Essential Mathematical Skills and Techniques); MAS253 (Mathematics for Engineering Modelling)

The following modules have this module as a prerequisite:

MAS340Mathematics (Computational Methods)


Outline syllabus

  • Non-linear Algebraic Equations: Bisection, one-point iteration, Newton's method, secant method.
  • Linear Algebraic equations: Gauss-Seidel method. Gaussian elimination, partial pivoting, LU decomposition.
  • Eigenvalues: Power method for the dominant eigenvalue.
  • Interpolation: Lagrange interpolation formula.
  • Data Fitting: Least-squares polynomial approximation for linear and quadratic fitting.
  • Numerical Differentiation and Integration: 3 point formulae for 1st and 2nd derivatives with errors. Trapezium rule, Simpson's rule
  • Ordinary Differential Equations (initial value problems): First order: Runge-Kutta: Euler 1, 2, 3; classical 4th order Runge-Kutta. Adaptation to second and higher order equations.
  • Ordinary Differential Equations (linear boundary value problems): Application to 2nd order equations of finite difference scheme using 3 point differentiation formulae.
  • Linear Programming: Graphical methods.



Aims

  • To consolidate previous mathematical knowledge.
  • To continue introducing students to mathematical and numerical techniques used in the area of Mechanical Engineering.

Learning outcomes

At the end of the course the student should be able to:
  • use basic iteration techniques to solve a non-linear algebraic equation;
  • apply iteration or direct methods to solve a system of linear equations;
  • calculate the dominant eigenvalue of an eigenvalue problem;
  • interpolate functions using the Lagrange interpolation formula;
  • apply a least squares polynomial approximation to fit data;
  • differentiate and integrate numerically;
  • solve initial value problems for 1st and 2nd order ordinary differential equations;
  • solve linear boundary value problems for 2nd order ordinary differential equations;
  • solve linear programming problems using graphical methods.

Teaching methods

Lectures, tutorials, problem solving


36 lectures, 9 tutorials

Assessment

One two-hour written examination.

Reading list

Type Author(s) Title Library Blackwells Amazon
B Atkinson, K.E. Introduction to Numerical Analysis Information Commons 518 (A) Blackwells Amazon
B Burden, R.L. and Douglas Faires, J Numerical Analysis 518 (B) Western Bank Library Blackwells Amazon
B Gerald, C.F. and Wheatley P.O. Applied Numerical Analysis Western Bank Library 518 (G) Blackwells Amazon

(A = essential, B = recommended, C = background.)

Most books on reading lists should also be available from the Blackwells shop at Jessop West.

Timetable

Thu 12:00 - 12:50 lecture   Diamond Building LT4