FACULTY OF ENGINEERING
MATH 301 – NUMERICAL ANALYSIS
ASSIGNMENT 1
Answer All Questions
[Submission Deadline: Sunday, 19th February, 2023; 12 noon. To be submitted in a group
of four (4) candidates per group]
1. Consider the function, f (x) = cos x – x = 0.
i.
Approximate a root of f(x) using Newton-Raphson’s Method using an initial
approximation of x = 0.
ii.
Explain whether there is convergence or not.
2. The bacterial concentration in a reservoir varies as C = 4e-2t + e-0.1t. Use Newton
Raphson’s Method to determine the time required for the bacteria concentration to be 0.5.
3. The current I in an electric circuit is given by I = 10e-t sin 2πt, where t is in seconds.
Using Newton – Raphson’s method, find the value of t correct to three decimal places for
I = 2 A.
4. The pressure of the gas corresponding to various volumes V is measured, and given by
the following data;
V/cm3
P/kg/cm3
50
64.7
60
51.3
70
40.5
90
25.9
100
78
Fit the data to the equation PVδ = C using the method of least squares.
Engr. M. T. Obutey (PhD)