DEPARTMENT
OF MATHEMATICS
FACULTYOF ENGINERING
ANDTECHNOLOGY
SRMUNIVERSITY
MAlOO3.TRANSFORMS
ANDBOUNDARY
VALUEPROBLEMS
(Gommonto CSE,SWE, ECE,EEE,lCEt EIE, TCE & MECHT)
SEMESTER
lll
yEAR: 2015-2016
ACADEMTG
LECTURE
SCHEME
/ PLAN
The objective
is to equipthe studentsof Engineering
andTechnology,
the knowledge
of Mathematics
and itsapplications
so as to enablethemto applythemfor solvingrealworldproblems.
The listof instructions
(provided
below)may be followedby a facultyrelatingto his/herownschedule
includeswarm-up period, controlled/freepractice,and the respectivefLedback of the classes
handled.The lessonplan has been formulatedbasedon high qualitylearningoutcomesand the
expectedoutcomesare as follows
Eachsubjectmusthavea minimumof 56 hours,whichin turn,45 hoursfor lectureand restof the
hoursfor tutorials.
Thefacultyhasto paymoreattentionin insisting
the studentsto have: 95 % class
attendance.
UNITI: PARTIALDIFFERENTIAL
EQUATIONS
Lect.
No
Lessonschedule
Learningoutcomes
Introduction to
Partial Differential
Equations,
Formation
of PDEby
-problems
elimination
of arbitrary
constants
L . 1 . 2 Formation of PDE by eliminationof Thestudentswillbe
problems
arbitrary
functionsable to use partial
1 . 1. 3
Methodsto solve the first order partial differential
equationsin
differential
equations-Typethe study of fluid
1, Type-2
L.1.4
Tutorial
mechanics,
heat
1 . 1 . 5 Methodsto solve the first order partial transfer,
differential
electromagnetic
equations- Type-3,Tvpe-4
theory
1 . 1 . 6 Reduction
quantum
and
to standardtypes
mechanics.
L.1.7
Lagrange's
LinearEquationsMethodof Grouping
1 . 1. 8
Lagrange'sLinear Equations-Methodof Theywillbe ableto
simulatemathematical
\[ultipliers
modelsusingpartial
1 . 1 . 9 Tutorial
differential
equations
1 . 1 . 1 0 Linear HomogeneousPartial Differential
Equations
of secondand Higherorderwith
constantco efficient
Type-1,Type-2
L.1.1
L . 1. 1 1 - Linear HomogeneousPartial Differential
Equations
of secondand Higherorderwith
constantco efficientType-3
Gumulative
hours
1
2
3
4
5
6
7
8
I
10
11
Page1 of4
L . 1 . 1 2 Linear HomogeneousPartial Differential
Equations
of secondand Higherorderwith
constantco efficient-Type4
1 . 1. 1 3 Classification
of secondorderlinearpDEvariableseparable
method
CYCLETEST-I:
12
13
DATE:05082 015
UNITll: |OURIERSERIES
L2.1
Introduction
of Fourierseries,
Dirichlet's
conditions
L.2.2
GeneralFourierseries
L.2.3
Fourierseriesof odd and Evenfunctionsin
(-n,n)
L.2.4
Fourierseriesof odd and Evenfunctionsin
(-l,l)
Studentswill be ableto
have good knowledge
L.2.5
Tutorial
in Fourierseries.
L.2.6
HalfRangesineandCosineseriesin
( 0 ,n )
L.2.7
HalfRangesineandCosineseriesin (0,/)
L.2.8
Parseval's
Theorem/ ldentity
L.2.9
Harmonic
Analysis
L . 2 . 1 0 Harmonic
Analysis- problems
L . 2 . 1 1 Tutorial
14
15
16
17
18
19
20
21
22
23
24
UNITlll: ONEDIMENSIONAL
WAVEANDHEATEQUAT|ON
1.3.1
Introductionto one dimensionalWave
Equation
Studentswillbe ableto
L . 3 . 2 Tutorial
be familiarwithone
1 . 3 . 3 One dimensional Wave Equation
dimensionalwave
Boundaryand initialvalue Problemswith equation
zerovelocity
t .3 . 4 Boundaryand initialvalue Problemswith
zerovelocity- problems
1 . 3 . 5 Boundaryand initialvalue problemswith
Nonzerovelocity
1 . 3 . 6 Boundaryand initialvalue Problemswith
Nonzerovelocityproblems
t .3 . 7 One dimensional
heat equation- problems Studentswill be ableto
withzeroboundarv
values
be familiar with one
1 . 3 . 8 Steadystate conditionsand zero boundary dimensional
heat
conditions
equation
1 . 3 . 9 Steady state conditions and Non-zero
boundary
conditions
1 . 3 . 1 0 Tutorial
1 . 3 . 1 1Slgedy and transientstates- problems
L . 3 . 1 2 Steadyandtransientstates- problems
cYcrrTEST_il:
25
26
27
28
29
30
31
32
33
34
35
36
DATE:02.09. 2015
SURPRISE
TEST
Page2 of 4
UNITlV: FOURTER
TRANSFORMS
L . 4 . 1 Introduction
to Fouriertransformsstatement
of Fourierintegraltheorem
L . 4 . 2 FourierTransformsand its
inversionformula
- problems
1.4.3 FourierSineTransforms
L.4.4
L.4.5
1.4.6
FourierCosineTransforms
Tutorial
37
38
39
40
Studentswill be ableto
gaingoodknowledge
in
the application of
cosine Fouriertransforms
n
L.4.7
Propertiesof Fouriertransforms
Properties of Fourier sine &
Transforms
1.4.8
Transforms
of simplefunctions
44
L.4.9
Tutorial
45
L.4.10| Convolution
Theorem
Convolution
TheoremL.4.11
problems
L . 4 . 1 2 Parseval's
ldentity;lntegralequations
42
43
46
47
48
.IONS
UNITV: Z-TRANSFORMS
ANDDTFFERENCE
EQUA
L.C.1
L.5.2
1.5.3
1.5.4
z-transforms-l
ntroduction
and definition
Elementary
properties
49
- Method1
lnverseZ-transforms
- Method2
InverseZ{ransforms
51
1.5.5
Tutorial
1.5.6
InverseZ{ransforms- Method3
Convolution
theorem
Convolution
theorem- problems
L.5.7
1.5.8
50
52
Students wilt
be
learningpropertiesof ztransforms and its
applicationsin solving
difference equation
whichwill helpthem in
applying
these
techniques
in signals&
systems
1.5.9
Formation
of difference
equation
1 . 5 . 1 0 Tutorial
53
u
55
56
57
58
1 . 5 . 1 1 Solutionsof differenceequationusing z_
transform
59
L . 5 . 1 2 Solutionsof ditferenceequationusing z_
- problems
transform
6o
MODELEXAM
12.10.2015
(Duration:3 Hours)
LASTWORKING
DAy : 06.11.201S
Page3 of4
TEXT BOOKS
l. Kreyszig.E, "Advanced Engineering Mathematics", 10th edition, John Wiley &
Singapore,
2012.
2. GrewalB.s, "Higher EnggMaths", Khannapublications,42ndEdition,2}l2.
Sons.
REFERENCES:
l. Sivaramakrishna
DasP. andVijayakumari.C,A text book of EngineeringMathematicsIII,Viji's Academy,20
I0
2. KandasamyP etal."EngineeringMathematics",Vol. II & Vol. III (4th revisededition),
S.Chand
& Co.,New Delhi,2000.
3. NarayananS.,Manicavachagom
Pillay T.K., Ramanaiah
G., o'Advanced
Mathematicsfor
Engineering students",VolumeII & m (2ndedition),S.Viswanathan
Printersandpublishers"
1992.
4. Venkataraman
M.K., "EngineeringMathematics"- Vol.III - A & B (13thedition),National
PublishingCo.,
Chennai,1998.
5. SankaraRao, "Introductionto PartialDifferentialEquations",2ndEdition,pHI Learningpvt.
Ltd.,2006.
WEBBASEDRESOURCES
http://enoq-maths.
com/home
InternalmarksTotal:50
Internalmarkssplitup: CycleTest 1: 10 Marks
ModelExam:20 Marks
CycleTest2: 10 Marks
Surprise
Test:5 marks
Attendance:
5 marks
Dr.A. Govindarajan
Professor
Professor& Head
CourseCo-ordinator
Department
of Mathematics
Email:oovindarajan.a@ktr.srmuniv.
ac.in
Email:hod.maths@ktr.srmuniv.ac.
in
Tel: +91-44-27417000
Ext:2701
Page4 of 4