MAT3700 Assignment 04 2026 Year Module 2026

UNIVERSITY OF SOUTH AFRICA (UNISA)
College of Science, Engineering and Technology



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MAT3700 ASSIGNMENT 04
Applied Mathematics — Fourier Series — Semester 1, 2026


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Module Code: MAT3700

Module Name: Applied Mathematics

Assignment No.: 04

Due Date: 2026

Semester: Semester 1, 2026




Submitted in partial fulfilment of the requirements for MAT3700
at the University of South Africa.

, UNISA | MAT3700 Assignment 04 — 2026



Question 1 (15 marks)


Question: A periodic function f (t) with period 2π is defined by


f (t) = t2 − t, (−π < t < π), f (t) = f (t + 2π).


Obtain a Fourier series expansion of the function.


Step 1: Write down the general Fourier series form


∞
a0 X
f (t) = + (an cos nt + bn sin nt)
2
n=1


where the coefficients are given by:

Z π Z π Z π
1 1 1
a0 = f (t) dt, an = f (t) cos nt dt, bn = f (t) sin nt dt.
π −π π −π π −π




Step 2: Compute a0


Z π Z π Z π 
1 2 1 2
a0 = (t − t) dt = t dt − t dt
π −π π −π −π


t2 is an even function, so:

π π
π3 2π 3
Z Z
2
t dt = 2 t2 dt = 2 · =
−π 0 3 3


t is an odd function, so:
Z π
t dt = 0
−π


Therefore:
1 2π 3 2π 2
a0 = · =
π 3 3
a0 π2
=
2 3


Step 3: Compute an



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