INDIVIDUAL MATLAB ASSIGNMENT

Overview of the MA2895 assessments - The assessment of MA2895 is a portfolio of assessments.

There are three parts in this assignment, one which just requires the creation of one script file, one which just requires the creation of one script file and one function file, and one which just requires the creation of one script file and three function files. Thus in total you create 7 m-files if you attempt all parts and in the submission instructions described in section 6 a zip file is created using Matlab which will be what is submitted. To get full marks you need to attempt all parts. Full details and the precise tasks are given later in this document and brie?y the tasks are as follows.

(1) A task which is mostly graphics in that you need to plot two ellipses and with given points on one of the ellipses you a draw line segment between each such point and the "nearest point" on the other ellipse. If everything is done then a table should also be created in the command window indicating the distances involved. This is the task which just requires the creation of one script file.

(2) A task to factorise, as far as possible, a given matrix A in the form

PAQ = LR

where L is a unit lower triangular matrix, R is upper triangular and where P and Q are both permutation matrices. The matrix P is associated with swapping rows and the matrix Q is associated with swapping columns and the criteria you should use to determine all these matrices is given later in this document. This task involves creating a function file which creates P, Q, L and R and a script file where the function is used on specific matrices.

(3) A task concerned with approximately determining a function u(x) on an interval [a, b] such that

u′′(x) = f(x), a < x < b, with u(a) = g₁ and u(b) = g₂.

There are a number of ways this problem can be tackled and for this assignment two approaches are involved. There is the use of the finite difference method as described in chapter 4 of the MA2715 notes and this involves the creation of a function file. It is actually possible here to give and expression for u(x) in terms of integrals involving f(x) although these integrals cannot usually be done exactly and need to be approximated. In this assignment this approach requires two function files, one to approximate an integral and the other which uses such approximations in the expression for u(x). A script file is also needed which uses the functions for specified test problems.

Attachment:- Assignment Files.rar