FT/GN/68/00/21.04.15
SRI VENKATESWARA COLLEGE OF ENGINEERING
COURSE DELIVERY PLAN - THEORY
LP: MA6351
Department of Applied Mathematics
B.E/B.Tech
Page 1 of 6
: Common to all Branches
Regulation: 2013 Rev. No: 00
Sub. Code / Sub. Name : MA6351 Transform and Partial Differential Equations
Date: 01.07.15
Unit II
: Fourier Series
Unit Syllabus: Dirichlet’s conditions – General Fourier series – Odd and even functions – Half
range sine series – Half range cosine series – Complex form of Fourier Series – Parseval’s
identity – Harmonic Analysis
Objective: To introduce Fourier series analysis this is central to many applications in
Engineering apart from its use in solving boundary value problems.
Session
Teaching
Topics to be covered
Ref
No *
Aids
Introduction to periodic functions, Bernoulli’s
1 – Ch.2;
1
LCD
Pg.2.1
– 2.4
formula, Fourier series and Dirichlet’s conditions.
2
General Fourier series and problems based on
that.
3
Fourier series for functions with arbitrary
intervals
4
Tutorial class
5
Introduction to odd and even functions and
Fourier series for odd and even functions
6
Half range cosine series and problems.
7
Half range sine series and problems.
8
Tutorial class
9
Complex form of Fourier series
10
RMS value of a function, Derivation of Parseval’s
Identity and Problems using Parseval’s Identity
11
Harmonic analysis for functions with period 2
and arbitrary period
12
Tutorial class
1 – Ch.2;
Pg.2.5 – 2.7 &
Pg.2.12 – 2.42
1 – Ch.2;
Pg.2.7 – 2.8 &
Pg.2.12 – 2.42
Worksheet
1 – Ch.2;
Pg.2.8 – 2.11 &
Pg.2.12 – 2.42
1 – Ch.2;
Pg.2.42 – 2.45 &
Pg.2.47 – 2.72
1 – Ch.2;
Pg.2.42 – 2.45 &
Pg.2.47 – 2.72
Worksheet
1 – Ch.2;
Pg.2.75 – 2.76 &
Pg.2.87 – 2.89
1 – Ch.2;
Pg.2.45 – 2.46 &
Pg.2.47 – 2.72
1 – Ch.2;
Pg.2.73 – 2.75 &
Pg.2.76 – 2.86
Worksheet
LCD
LCD
LCD/BB
LCD
LCD
LCD
LCD/BB
LCD
LCD
LCD
LCD/BB
Content beyond syllabus covered (if any):
Application to specific area’s included (like medical electronics) heat pulse.
Course Outcome 1: The student will be able to apply Fourier series analysis in Engineering
problems.
* Session duration: 50 minutes
FT/GN/68/00/21.04.15
SRI VENKATESWARA COLLEGE OF ENGINEERING
COURSE DELIVERY PLAN - THEORY
Page 2 of 6
Sub. Code / Sub. Name: MA6351 Transform and Partial Differential Equations
Unit III
: Applications of Partial Differential Equations
Unit Syllabus: Classification of PDE – Method of separation of variables - Solutions of one
dimensional wave equation – One dimensional equation of heat conduction – Steady state
solution of two dimensional equation of heat conduction (excluding insulated edges).
Objective: To know how to apply Fourier series to get the solution of wave and heat equations.
Session
Teaching
Topics to be covered
Ref
No *
Aids
13
Introduction and Classification of PDE.
5 – Ch.19;
Pg. 19.1 – 19.3
LCD
14
Method of separation of variables.
2 – Ch.18;
Pg. 657 – 658
LCD
1 – Ch.3;
Pg.3.6 – 3.8
LCD
1 – Ch.3;
Pg.3.10 – 3.60
LCD
Worksheet
LCD/BB
1 – Ch.3;
Pg.3.63 – 3.65
LCD
1 – Ch.3;
Pg.3.65 – 3.113
LCD
Worksheet
LCD/BB
15
16
17
18
19
20
Solutions of one dimensional wave equation by method
of separation of variables
Problems on wave equation with the given initial
and boundary conditions
Tutorial class
Solution of one-dimensional heat equation by
method of separation of variables
Problems on heat equation with the given initial
and boundary conditions
Tutorial class
Continuous Assessment Test-I
21
Steady state solution of two dimensional equation of
heat conduction by method of separation of variables
1 – Ch.3;
Pg.3.117 – 3.119
LCD
22
Problems on Laplace equation for a finite plate.
1 – Ch.3;
Pg.3.119 – 3.163
LCD
23
Problems on Laplace equation for a semi - infinite
plate.
1 – Ch.3;
Pg.3.119 – 3.163
LCD
24
Tutorial class
Worksheet
LCD/BB
Content beyond syllabus covered (if any):
Knowledge of heat transfer in circular plate is included.
Course Outcome 2:
The student will be able to classify and solve wave equations and heat equations.
* Session duration: 50 mins
FT/GN/68/00/21.04.15
SRI VENKATESWARA COLLEGE OF ENGINEERING
COURSE DELIVERY PLAN - THEORY
Page 3 of 6
Sub. Code / Sub. Name: MA6351 Transform and Partial Differential Equations
Unit IV
: Fourier Transforms
Unit Syllabus: Statement of Fourier integral theorem – Fourier transform pair – Fourier sine and
cosine transforms – Properties – Transforms of simple functions – Convolution theorem –
Parseval’s identity.
Objective: To acquaint the student with Fourier transform techniques used in wide variety of
situations.
Session
Teaching
Topics to be covered
Ref
No *
Aids
Introduction to infinite Fourier transform and
1 – Ch.4;
25
LCD
Pg.4.1 – 4.2
Fourier integral theorem
26
Fourier transforms pair and problems.
27
More problems on Fourier transform pair
28
Tutorial class
29
Fourier cosine and sine transform and problems
30
31
More problems on Fourier sine and cosine
transform.
Properties of Fourier transforms, Fourier sine
transforms and cosine transforms.
32
Tutorial class
33
Transforms of simple functions and problems.
34
35
36
Derivation of Convolution theorem and Parseval’s
identity for Fourier transforms
Problems using Parseval’s identity and convolution
theorem
Tutorial class
1 – Ch.4;
Pg.4.4 – 4.5 &
Pg.4.11 – 4.15
1 – Ch.4;
Pg.4.23 – 4.26
Worksheet
1 – Ch.4;
Pg.4.5 – 4.6 &
Pg.4.15 – 4.23
1 – Ch.4;
Pg.4.23 – 4.26
LCD
LCD
LCD/BB
LCD
LCD
1 – Ch.4;
Pg.4.26 – 4.28
LCD
Worksheet
LCD/BB
1 – Ch.4;
Pg.4.29 – 4.31 &
Pg.4.37 – 4.41
1 – Ch.4;
Pg.4.31 – 4.33
LCD
LCD
1 – Ch.4;
Pg.4.37 – 4.41
LCD
Worksheet
LCD/BB
Content beyond syllabus covered (if any): Nil
Course Outcome 3:
Students will be able to solve problems related to engineering applications by using Fourier
transform techniques.
* Session duration: 50 mins
FT/GN/68/00/21.04.15
SRI VENKATESWARA COLLEGE OF ENGINEERING
COURSE DELIVERY PLAN - THEORY
Page 4 of 6
Sub. Code / Sub. Name: MA6351 Transform and Partial Differential Equations
Unit V
: Z -Transforms and Difference Equations
Unit Syllabus: Z- Transforms - Elementary properties – Inverse Z - transform (using partial
fraction and residues) – Convolution theorem - Formation of difference equations – Solution of
difference equations using Z - transform.
Objective: To develop Z transform techniques for discrete time systems.
Session
Teaching
Topics to be covered
Ref
No *
Aids
Introduction to Z- transforms and Elementary
1 – Ch.5;
37
LCD
Pg.5.1 – 4.12
properties of Z-transforms
Problems based on elementary properties of Z1 – Ch.5;
38
LCD
Pg.5.12 – 5.19
transforms
39
Initial and Final value theorems on Z – transforms.
1 – Ch.5;
Pg.5.4 – 5.5
LCD
40
Tutorial class
Worksheet
LCD/BB
41
Inverse Z – transform using partial fraction
42
Inverse Z – transform using residues
43
Derivation of Convolution theorem.
44
Inverse Z – transform using Convolution theorem.
45
Tutorial class
1 – Ch.5;
Pg.5.26 – 5.34
1 – Ch.5;
Pg.5.26 – 5.34
LCD
LCD
1 – Ch.5;
Pg.5.5 – 5.7
1 – Ch.5;
Pg.5.20 – 5.23
LCD
LCD
Worksheet
Continuous Assessment Test-II
46
Formation of difference equations
47
Solution of difference equation using Z-transforms
48
Tutorial class
2 – Ch.30;
Pg.1084 – 1086
1 – Ch.5;
Pg.5.27 &
Pg.5.34 – 5.40
Worksheet
LCD
LCD
LCD/BB
Content beyond syllabus covered (if any):
Application in system engineering included.
Course Outcome 4:
Students are able to understand the discrete transform applied to Engineering problems.
* Session duration: 50 mins
FT/GN/68/00/21.04.15
SRI VENKATESWARA COLLEGE OF ENGINEERING
COURSE DELIVERY PLAN - THEORY
Page 5 of 6
Sub. Code / Sub. Name: MA6351 Transform and Partial Differential Equations
Unit I
: Partial Differential Equations
Unit Syllabus: Formation of partial differential equations – Singular integrals - Solutions of
standard types of first order partial differential equations - Lagrange’s linear equation - Linear
partial differential equations of second and higher order with constant coefficients of both
homogeneous and non-homogeneous types.
Objective: To introduce the effective mathematical tools for the solutions of partial differential
equations that model several physical processes.
Session
Teaching
Topics to be covered
Ref
No *
Aids
Introduction to PDE and Formation of PDE by
1 – Ch.1;
49
elimination of arbitrary constants and by elimination of
LCD
Pg.1.1 – 1.21
arbitrary functions.
1 – Ch.1;
Pg.1.1 – 1.21
LCD
Worksheet
LCD/BB
50
Formation of PDE by elimination of arbitrary functions.
51
Tutorial class
52
Various solutions of a general PDE – complete, singular,
particular and general integrals
53
Solving standard types of PDEs of the form F(p, q) = 0
and F(z, p,q)=0.
1 – Ch.1;
Pg.1.21 – 1.23
1 – Ch.1;
Pg.1.23 – 1.25 &
Pg.1.28 – 1.50
54
Solving standard types of PDEs of the form
z = px+qy+f(p, q) and F1(x, p)=F2(y,q).
1 – Ch.1;
Pg.1.23 – 1.25 &
Pg.1.28 – 1.50
55
Equations reducible to standard forms
56
Tutorial class
57
Solving Lagrange’s linear equation by Method of
multipliers
58
59
60
Tutorial class
Solution of homogeneous linear partial differential
equations of second and higher order with constant
coefficients.
Solution of non-homogeneous linear partial differential
equations of second and higher order with constant
coefficients.
Continuous Assessment Test-III
LCD
LCD
LCD
1 – Ch.1;
Pg.1.26 – 1.27 &
Pg.1.28
– 1.50
Worksheet
LCD/BB
1 – Ch.1;
Pg.1.51 – 1.71
LCD
Worksheet
LCD/BB
1 – Ch.1;
Pg.1.71 – 1.98
LCD
1 – Ch.1;
Pg.1.71 – 1.98
LCD
LCD
Content beyond syllabus covered (if any): Nil
Course Outcome 5: Students are able to formulate and solve some of the physical problems
involving Partial Differential Equations.
* Session duration: 50 mins
Sub Code / Sub Name: MA6351 Transform and Partial Differential Equations
FT/GN/68/00/21.04.15
SRI VENKATESWARA COLLEGE OF ENGINEERING
COURSE DELIVERY PLAN - THEORY
Mapping CO – PO:
PO1 PO2
CO1
A
CO2
A
CO3
B
CO4
B
CO5
PO3
C
PO4
PO5
PO6
PO7
PO8
Page 6 of 6
PO9
PO10
PO11
PO12
A – Excellent ; B – Good ; C - Average
REFERENCES:
1. Veerarajan. T., "Transforms and Partial Differential Equations", Second reprint, Tata MGraw
Hill Education Pvt. Ltd., New Delhi, 2012.
2. Grewal. B.S., "Higher Engineering Mathematics", 42nd Edition, Khanna Publishers, Delhi,
2012.
3. Narayanan.S., Manicavachagom Pillay.T.K and Ramanaiah.G "Advanced Mathematics for
Engineering Students" Vol. II & III, S.Viswanathan Publishers Pvt Ltd. 1998.
4. Bali.N.P and Manish Goyal, "A Textbook of Engineering Mathematics", 7th Edition, Laxmi
Publications Pvt Ltd , 2007.
5. Ramana.B.V., "Higher Engineering Mathematics", Tata Mc-Graw Hill Publishing Company
Limited, New Delhi, 2008.
6. Glyn James, "Advanced Modern Engineering Mathematics", 3rd Edition, Pearson Education,
2007.
7. Erwin Kreyszig, "Advanced Engineering Mathematics", 8th Edition, Wiley India, 2007.
8. Ray Wylie. C and Barrett.L.C, "Advanced Engineering Mathematics" Sixth Edition, Tata
McGraw Hill Education Pvt Ltd, New Delhi, 2012.
9. Datta.K.B., "Mathematical Methods of Science and Engineering", Cengage Learning India
Pvt Ltd, Delhi, 2013.
Prepared by
Approved by
Dr M RADHAKRISHNAN
DR. R. MUTHUCUMARASWAMY
Assistant Professor
Professor & Head
01.07.2015
01.07.2015
Signature
Name
Designation
Date
Remarks *:
The same Lesson Plan may be used for MA6351 Transforms and Partial Differential Equations in the
subsequent semester.
Remarks *:
* If the same lesson plan is followed in the subsequent semester/year it should be mentioned and
signed by the Faculty and the HOD