Computing
MM245: Numerical Analysis I (5 ECTS)
This course teaches the basics of numerical analysis, with associated laboratories using MATLAB. Topics covered include: approximations & errors, propagation of errors, finding roots of a function, numerical interpolation, numerical integration, numerical methods for linear systems of equations, and numerical methods for simple differential equations
Taught in Semester(s) I. Examined in Semester(s) I.
Workload: 34 hours (24 Lecture hours, 10 Lab hours).
Module Learning Outcomes.
On successful completion of this module the learner should be able to:
- Carry out elementary arithmetic operations in Matlab; write iterative programs in Matlab; compose code in Matlab using basic control structures such as IF statements; plot results in 2 dimensional plots in Matlab.
- Determine the root(s) of a function in a certain interval using a number of methods; describe the convergence properties of the method used; estimate the error and accuracy of the result.
- Carry out basic numerical interpolation; determine the error bounds on such interpolation.
- Use basic Newton-Cotes methods to estimate a definite integral; calculate the error in the resulting approximation; program these methods in Matlab.
- Use simple methods in numerical linear algebra for finding eigenvalues and eigenvectors.
- Estimate the solution to a simple differential equation using the Euler method; use this method to obtain the value of the function at a point in the region of definition; estimate the resulting error.
Indicative Content
- Scientific programming in Matlab.
- Root finding: iterative methods, convergence, order, Newton's method.
- Interpolation: Lagrange form and error.
- Numerical integration: some Newton-Cotes formulae with error (Trapezoid rule).
- Some numerical methods in linear algebra: Gauss elimination, Jacobi Iteration.
- Some numerical methods for ordinary differential equations: the Euler method, the improved Euler method.
Module Resources
Glyn James : 'Modern Engineering Mathematics' Pearson-Prentice Hall, 4th edition.
Glyn James: 'Advanced Modern Engineering Mathematics', Prentice Hall, 4th Edition.
MATLAB (or SCILAB or OCTAVE)
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