MAS254 Computational and Numerical Methods
|Semester 2, 2011/12||10 Credits|
|Lecturer:||Dr Istvan Ballai||Timetable||Reading List|
Prerequisites: MAS253 (Mathematics for Engineering Modelling)
The following modules have this module as a prerequisite:
|MAS340||Mathematics (Computational Methods)|
- 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.
- To consolidate previous mathematical knowledge.
- To continue introducing students to mathematical and numerical techniques used in the area of Mechanical Engineering.
Learning outcomesAt 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.
Lectures, tutorials, problem solving
36 lectures, 9 tutorials
|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 on Mappin Street.
|Mon||12:00 - 12:50||lecture||Richard Roberts Auditorium|
|Tue||09:00 - 09:50||lecture||Arts Tower Lecture Theatre 4|
|Tue||10:00 - 10:50||tutorial||Arts Tower Lecture Theatre 4|
|Wed||09:00 - 09:50||lecture||Richard Roberts Auditorium|