APM2611
ASSIGNMENT 4 2025
UNIQUE NO.
DUE DATE: 24 SEPTEMBER 2025
, lOMoARcPSD|21997160
ASSIGNMENT 04
Due date: Wednesday, 24 September 2025
ONLY FOR YEAR MODULE
Series solutions, Laplace transforms and Fourier series, solving PDE’s by separation of
variables.
Answer all the questions. Show all your own and personalized workings, you get ZERO to
a question if we see that you have copied someone’s else solution word by word.
You must submit your assignment via myUnisa, and note that only PDF files will be ac-
cepted.
Note that all the questions will be marked therefore, it is highly recommended to attempt all of
them.
Question 1
Use the power series method to solve the initial value problem:
00 0 0
y − xy + 4y = 2, y (0) = 0, y (0) = 1.
Question 2
Consider the function
sin t 0≤ t <π
f (t ) = sin(t − π ) π ≤ t < 2π .
0 otherwise
(2.1) Find the Laplace transform of f (t ) by first principles, the table of integrals and
Z b Z b −π
f (t ) sin(t− π ) dt = f (τ + π) sin τ d τ .
a a−π
(2.2) Express f (t ) in terms of the Heaviside step function and use the table of Laplace
transforms to calculate L f (t ).
28
ASSIGNMENT 4 2025
UNIQUE NO.
DUE DATE: 24 SEPTEMBER 2025
, lOMoARcPSD|21997160
ASSIGNMENT 04
Due date: Wednesday, 24 September 2025
ONLY FOR YEAR MODULE
Series solutions, Laplace transforms and Fourier series, solving PDE’s by separation of
variables.
Answer all the questions. Show all your own and personalized workings, you get ZERO to
a question if we see that you have copied someone’s else solution word by word.
You must submit your assignment via myUnisa, and note that only PDF files will be ac-
cepted.
Note that all the questions will be marked therefore, it is highly recommended to attempt all of
them.
Question 1
Use the power series method to solve the initial value problem:
00 0 0
y − xy + 4y = 2, y (0) = 0, y (0) = 1.
Question 2
Consider the function
sin t 0≤ t <π
f (t ) = sin(t − π ) π ≤ t < 2π .
0 otherwise
(2.1) Find the Laplace transform of f (t ) by first principles, the table of integrals and
Z b Z b −π
f (t ) sin(t− π ) dt = f (τ + π) sin τ d τ .
a a−π
(2.2) Express f (t ) in terms of the Heaviside step function and use the table of Laplace
transforms to calculate L f (t ).
28
