THIS NOTES ARE ABOUT DIFFERENTIAL EQUATIONS

1. CLO3
Develop the understanding of
separation of variables and
the use of Fourier series to
solve PDEs.
C3 PLO2
Subject MA-225 Differential Equations and Transforms
Reference
Book
Advanced Engineering Mathematics, 10th Ed.
by Erwin Kreyszig
Topic Fourier Series
Chapter 11
Exercise 11.1
Instructor Dr. Arshi Khalid
Lecture # 1 (ODL lesson via MS Teams)
CLOs
Description
Domain &
Level
PLO
mapping

2. Why Fourier Series?
Its in the syllabus !!
Periodic Phenomena occurs quite frequently in the real world
• Rhythm of heart under normal condition
• Rotating machines
• Motors
• Rotation of earth
Useful Tool
 To express/transform periodic function into simple sine and cosine waves
 To handle piecewise continuous function

98. 


sin
cos i
ei


Using the Euler’s formula
i

99. 


























 



 












dx
e
x
f
c
dx
nx
i
nx
x
f
c
nxdx
x
f
i
nxdx
x
f
c
ib
a
c
inx
n
n
n
n
n
n
)
(
1
2
1
)
sin
)(cos
(
1
2
1
sin
)
(
1
cos
)
(
1
2
1
2
/
)
(