COT 305 MATHEMATICS 3 Exam 2026

About this paper

COT 305: End-of-semester examination for COT305, Mathematics III, Department of Computer Engineering, College of Technology, University of Buea, First Semester 2025/2026 (31 January 2026), instructors Mbaptc/Nana/Suh -- a duplicate copy of the same paper as ID 2957. Exercise 1 (10 marks) models world population growth of 1.12% a year from 7.6 billion in 2017 as a difference equation, solving it and projecting the 2050 population. Exercise 2 (32 marks) covers differential equations: finding the general solution of a linear system of first-order ODEs (dx1/dt=x1+x2, dx2/dt=4x1+x2), then for y''-7y'+10y=0 verifying that e^(2x) and e^(5x) are solutions, computing their Wronskian to test fundamentality, deducing the general solution, and solving an initial value problem. Exercise 3 (28 marks) uses the Laplace transform to solve y''+4y=3sin(t) with given initial conditions, then computes the Fourier coefficients and series of f(x)=cos(x/2) on [-pi,pi], explains convergence of the series to f, and deduces the sum of the series sum 1/(4n^2-1) by evaluating at x=pi. A table of Laplace transforms and inverses is provided as reference.