MAS254 Computational and Numerical Methods
|Semester 2, 2019/20||10 Credits|
|Lecturer:||Dr Gary Verth||Timetable||Reading List|
Prerequisites: MAS152 (Essential Mathematical Skills and Techniques); 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
One two-hour written examination.
|B||Atkinson, K.E.||Introduction to Numerical Analysis||Information Commons 518 (A)||Blackwells||Amazon|
|B||Burden, R.L. and Douglas Faires, J||Numerical Analysis|
|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.
|Mon||14:00 - 14:50||lecture||Hicks Lecture Theatre 1|
|Mon||15:00 - 15:50||tutorial||Hicks Lecture Theatre 1|
|Fri||11:00 - 11:50||lecture||Diamond Building LT4|
|Fri||12:00 - 12:50||tutorial||Diamond Building LT4|