MAT3700 Assignment 04 Year Module 2026

UNIVERSITY OF SOUTH AFRICA
College of Science, Engineering and Technology


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MAT3700: Applied Mathematics

Assignment 04 — Semester 1, 2026

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MAT3700
Module Code:
Applied Mathematics
Module Name:
Assignment 04
Assignment:
2026
Due Date:
40
Total Marks:




Submitted in partial fulfilment of the requirements for MAT3700 — UNISA 2026

, UNISA | MAT3700 Assignment 04 — 2026



Question 1: Fourier Series of f (t) = t2 − t (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: 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 1
a0 = (t2 − t) dt = t2 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




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