Unit Syllabus: Fourier Series

DOC/LP/01/28.02.02

/ LESSON PLAN / LP- MA2211
Rev. No: 00
Date:27.06.2012
Page 1 of 6
SUB CODE & NAME:MA2211 TRANSFORMSAND PARTIAL
DIFFERENTIAL EQUATIONS
UNIT:I SEMESTER : III
BRANCH:COMMON TO ALL BRANCHES

Unit syllabus: Fourier Series

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 identify – Harmonic Analysis.

Objective: To know about the Fourier’s series and its applications.

Session
No / Topics to be covered / Time / Ref / Teaching Method
1 / Introduction to periodic functions
Introduction about Fourier series / 20m
30m / 1,2,3,4 / BB
2 / Dirichlet’s conditions for Fourier series
Derivation of Fourier coefficients or Euler’s constants / 20m
30m / 1,2,3,4 / BB
3 / Fourier series for functions with arbitrary intervals / 50m / 1,2,3,4 / BB
4 / Tutorial class / 50m / 1,2,3,4 / BB
5 / Introduction to odd and even functions
Fourier series for odd and even functions / 25m
25m / 1,2,3,4 / BB
6 / Half range cosine series
Half range sine series / 50m / 1,2,3,4 / BB
7 / Problems on arbitrary interval-half range series / 50m / 1,2,3,4 / BB
8 / Complex form of Fourier series / 50m / 1,2,3,4 / BB
9 / RMS value of a function, Derivation of Parseval’s formula
Problems using Parseval’s formula / 20m
30m / 1,2,3,4 / BB
10 / Harmonic analysis for functions with (i) period 2
(ii) arbitrary period / 50m / 1,2,3,4 / BB
11 / More problems solved in Harmonic Analysis. / 50m / 1,2,3,4 / BB
12 / Summarizing the unit / 50m / 1,2,3,4 / BB
/ LESSON PLAN / LP- MA2211
Rev. No: 00
Date: 27.06.2012
Page 2 of 6
SUB CODE & NAME: MA2211 TRANSFORMSAND PARTIAL
DIFFERENTIAL EQUATIONS
UNIT: II SEMESTER : III
BRANCH:COMMON TO ALL BRANCHES

Unit syllabus: Fourier TransformS

Fourier integral theorem (without proof) – Fourier transform pair – Sine and
Cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.

Objective: To know how to obtain an infinite Fourier transform and its applications

Session
No / Topics to be covered / Time / Ref / Teaching Method
13 / Infinite Fourier transform
Fourier integral theorem / 20m
30m / 1,2,3,5 / BB
14 / Fourier transform pairs / 50m / 1,2,3,5 / BB
15 / Fourier cosine and sine transform / 50m / 1,2,3,5 / BB
16 / Properties of Fourier transforms / 50m / 1,2,3,5 / BB
17 / Transforms of simple functions / 50m / 1,2,3,5 / BB
18 / Transforms of derivatives / 50m / 1,2,3,5 / BB
19 / Convolution theorem for Fourier transforms / 50m / 1,2,3,5 / BB
20 / Problems using convolution theorem / 50m / 1,2,3,5 / BB
21 / Parseval’s identity / 50m / 1,2,3,5 / BB
22 / Problems using Parseval’s identity / 50m / 1,2,3,5 / BB
23 / CAT-I / 75m
/ LESSON PLAN / LP- MA2211
Rev. No: 00
Date: 27.06.2012
Page 3 of 6
SUB CODE & NAME: MA2211 TRANSFORMSAND PARTIAL
DIFFERENTIAL EQUATIONS
UNIT: III SEMESTER : III
BRANCH:COMMON TO ALL BRANCHES

Unit syllabus:PARTIAL DIFFERENTIAL EQUATIONS

Formation of partial differential equations – Lagrange’s linear equation – Solutions of standard types of first order partial differential equations - Linear partial differential equations of second and higher order with constant coefficients.

Objective: To know how to form and solve partial differential equations

Session
No / Topics to be covered / Time / Ref / Teaching Method
24 / Introduction to PDE / 50m / 1,2,3,5 / BB
25 / Formation of PDE by elimination of arbitrary constants / 50m / 1,2,3,5 / BB
26 / Formation of PDE by elimination of arbitrary functions of one variable / 50m / 1,2,3,5 / BB
27 / Formation of PDE by elimination of arbitrary functions of two variables / 50m / 1,2,3,5 / BB
28 / Various solutions of a general PDE – complete, singular, particular and general integrals / 50m / 1,2,3,5 / BB
29 / Solving standard types of PDE - Type 1
- Type 2 / 25m
25m / 1,2,3,5 / BB
30 / Solving standard types of PDE - Type 3
- Type 4 / 25m
25m / 1,2,3,5 / BB
31 / Equations reducible to standard forms / 50m / 1,2,3,5 / BB
32 / Lagrange’s linear equation-Method of multipliers / 50m / 1,2,3,5 / BB
33 / Lagrange’s linear equation-Method of grouping / 50m / 1,2,3,5 / BB
34 / Homogeneous linear partial differential equations of second and higher order with constant coefficients. / 50m / 1,2,3,5 / BB
35 / Non-homogeneous linear partial differential equations of second and higher order with constant coefficients. / 50m / 1,2,3,5 / BB
36 / Summarizing the unit / 50m / BB
/ LESSON PLAN / LP- MA2211
Rev. No: 00
Date: 27.06.2012
Page 4 of 6
SUB CODE & NAME: MA2211 TRANSFORMSAND PARTIAL
DIFFERENTIAL EQUATIONS
UNIT: IV SEMESTER : III
BRANCH:COMMON TO ALL BRANCHES

Unit syllabus: APPLICATIONS of partial differential equations

Solutions of one dimensional wave equation – One dimensional equation of heat conduction – Steady state solution of two-dimensional equation of heat conduction (Insulated edges excluded) – Fourier series solutions in Cartesian coordinates.

Objective: To know how to apply Fourier series to get the solution to wave and heat equations.

Session
No / Topics to be covered / Time / Ref / Teaching Method
38 / Introduction about wave equation and Method of separation of variables / 50m / 1,2,3 / BB
39 / Derivation of one-dimensional wave equation / 50m / 1,2,3 / BB
40 / Solution of wave equation-Method of separation of variables / 50m / 1,2,3 / BB
41 / Problems on wave equation with the given initial and boundary conditions / 50m / 1,2,3 / BB
42 / Derivation of one-dimensional heat equation / 50m / 1,2,3 / BB
43 / Solution of one-dimensional heat equation / 50m / 1,2,3 / BB
44 / Problems on heat equation with the given initial and boundary conditions / 50m / 1,2,3 / BB
45 / CAT- II / 75m / 1,2,3
46 / Derivation of two-dimensional heat equation-Steady state heat flow in 2D-Laplace equation / 20m
30m / 1,2,3 / BB
47 / Solution of Laplace equation in Cartesian form
Laplace equation for a square plate / 50m / 1,2,3 / BB
48 / Laplace equation for a semi-infinite plate / 40m / 1,2,3
/ LESSON PLAN / LP- MA2211
Rev. No: 00
Date: 27.06.2012
Page 5 of 6
SUB CODE & NAME: MA2211 TRANSFORMSAND PARTIAL
DIFFERENTIAL EQUATIONS
UNIT: V SEMESTER : III
BRANCH:COMMON TO ALL BRANCHES

Unit syllabus:Z -TRANSFORMs AND DIFFERENCE Equations

Z-transforms - Elementary properties – Inverse Z-transform – Convolution theorem -Formation of difference equations – Solution of difference equations using Z-transform.

Objective: To know about Z-transforms and its applications in difference equation.

Session
No / Topics to be covered / Time / Ref / Teaching Method
49 / Introduction to Z- transforms / 50m / 1,2,3,4 / BB
50 / Elementary properties of Z-transforms / 50m / 1,2,3,4 / BB
51 / Elementary properties of Z-transforms / 50m / 1,2,3,4 / BB
52 / Inverse Z- transform / 50m / 1,2,3,4 / BB
53 / Convolution theorem -Derivation / 50m / 1,2,3,4 / BB
54 / Convolution theorem-problems / 50m / 1,2,3,4 / BB
55 / Formation of difference equations / 50m / 1,2,3,4 / BB
56 / Formation of difference equations / 50m / 1,2,3,4 / BB
57 / Solution of difference equation using Z-transforms / 50m / 1,2,3,4 / BB
58 / Solution of difference equation using Z-transforms / 50m / 1,2,3,4 / BB
59 / Summarizing the unit / 50m / 1,2,3,4 / BB
60 / CAT-III / 75m
/ LESSON PLAN / LP- MA2211
Rev. No: 00
Date: 27.06.2012
Page 6 of 6
SUB CODE & NAME: MA2211 TRANSFORMSAND PARTIAL
DIFFERENTIAL EQUATIONS
SEMESTER : III
BRANCH:COMMON TO ALL BRANCHES

Course Delivery Plan:

Week / 1 / 2 / 3 / 4 / 5 / 6 / 7 / 8 / 9 / 10 / 11 / 12 / 13 / 14 / 15
I II / I II / I II / I II / I II / I II / I II / I II / I II / I II / I II / I II / I II / I II / I II
Units

Text Book

Grewal, B.S, “Higher Engineering Mathematic”, 40th Edition, Khanna

Publishers, Delhi, (2007).

Reference BOOKS

Bali.N.P and Manish Goyal, “A Textbook of Engineering Mathematic”, 7th

Edition, Laxmi Publications(P) Ltd. (2007)

Ramana.B.V., “Higher Engineering Mathematics”, Tata Mc-GrawHill

Publishing Company limited, New Delhi (2007).

Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition,

Pearson Education (2007).

Erwin Kreyszig, “Advanced Engineering Mathematics”, 8th edition, Wiley

India (2007).

Prepared by / Approved by
Signature
Name / G. Satheesh Kumar / Dr.R. Muthucumaraswamy
Designation / Assistant professor / Prof & Head – AM