KNF2033 Engineering Mathematics III

ASSIGNMENT 3: VECTOR DIFFRENTIAL

Instruction:

a) Write your answers using Microsoft Word.b) Print your answer on A4 paper and submit into my pigeonhole before

25th October 2013.

Questions:

1) Consider the temperature at a point (x, y, z) in a rectangular box is given by T (¿0C)=10+xyz (1−x)(2− y )(3−z )¿, 0≤ x≤1cm,0≤ y≤2cm,0≤ z≤3cm. If a fly is currently at location (0.5, 1, 1), in which direction should it fly to cool off as rapidly as possible? Find the minimum length of the path it should take for ∆T=100C. (9 marks)

2) Suppose the Earth is moving in circular orbit (which is inaccurate) around the Sun. By using vector valued function, develop mathematical model representing velocity, acceleration and central force exerted by the Earth on the Sun. (6 marks)