Department of Applied Mathematics - Home - Sri …€¦ · · 2015-09-09FT/GN/68/00/21.04.15 SRI VENKATESWARA COLLEGE OF ENGINEERING COURSE DELIVERY PLAN - THEORY Page 1 of 6 Department

FT/GN/68/00/21.04.15 SRI VENKATESWARA COLLEGE OF ENGINEERING

COURSE DELIVERY PLAN - THEORY Page 1 of 6

Department of Applied Mathematics B.E/B.Tech : Information Technology Regulation: 2013

Sub. Code / Sub. Name : MA6351 Transform and Partial Differential Equations

Unit II : Fourier Series

LP: MA6351

Rev. No: 00

Date: 01.07.15

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 No *

Topics to be covered Ref Teaching

Aids

1 Introduction to periodic functions, Bernoulli’s formula, Fourier series and Dirichlet’s conditions.

1 – Ch.2; Pg.2.1 – 2.4 LCD

2 General Fourier series and problems based on that.

1 – Ch.2; Pg.2.5 – 2.7 & Pg.2.12 – 2.42

LCD

3 Fourier series for functions with arbitrary intervals

1 – Ch.2; Pg.2.7 – 2.8 & Pg.2.12 – 2.42

LCD

4 Tutorial class Worksheet LCD/BB

5 Introduction to odd and even functions and Fourier series for odd and even functions

1 – Ch.2; Pg.2.8 – 2.11 & Pg.2.12 – 2.42

LCD

6 Half range cosine series and problems. 1 – Ch.2;

Pg.2.42 – 2.45 & Pg.2.47 – 2.72

LCD

7 Half range sine series and problems. 1 – Ch.2;

Pg.2.42 – 2.45 & Pg.2.47 – 2.72

LCD


9 Complex form of Fourier series 1 – Ch.2;

Pg.2.75 – 2.76 & Pg.2.87 – 2.89

LCD

10 RMS value of a function, Derivation of Parseval’s Identity and Problems using Parseval’s Identity

1 – Ch.2; Pg.2.45 – 2.46 & Pg.2.47 – 2.72

LCD

11 Harmonic analysis for functions with period 2π and arbitrary period

1 – Ch.2; Pg.2.73 – 2.75 & Pg.2.76 – 2.86

LCD


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



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 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

15 Solutions of one dimensional wave equation by method of separation of variables

1 – Ch.3; Pg.3.6 – 3.8 LCD

16 Problems on wave equation with the given initial and boundary conditions

1 – Ch.3; Pg.3.10 – 3.60 LCD


18 Solution of one-dimensional heat equation by method of separation of variables

1 – Ch.3; Pg.3.63 – 3.65 LCD

19 Problems on heat equation with the given initial and boundary conditions

1 – Ch.3; Pg.3.65 – 3.113 LCD


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


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




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 No *


Aids

25 Introduction to infinite Fourier transform and Fourier integral theorem

1 – Ch.4; Pg.4.1 – 4.2 LCD

26 Fourier transforms pair and problems. 1 – Ch.4;

Pg.4.4 – 4.5 & Pg.4.11 – 4.15

LCD

27 More problems on Fourier transform pair 1 – Ch.4; Pg.4.23 – 4.26 LCD


29 Fourier cosine and sine transform and problems 1 – Ch.4;

Pg.4.5 – 4.6 & Pg.4.15 – 4.23

LCD

30 More problems on Fourier sine and cosine transform.

1 – Ch.4; Pg.4.23 – 4.26 LCD

31 Properties of Fourier transforms, Fourier sine transforms and cosine transforms.

1 – Ch.4; Pg.4.26 – 4.28 LCD


33 Transforms of simple functions and problems. 1 – Ch.4;

Pg.4.29 – 4.31 & Pg.4.37 – 4.41

LCD

34 Derivation of Convolution theorem and Parseval’s identity for Fourier transforms

1 – Ch.4; Pg.4.31 – 4.33 LCD

35 Problems using Parseval’s identity and convolution theorem

1 – Ch.4; Pg.4.37 – 4.41 LCD


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




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 No *


Aids

37 Introduction to Z- transforms and Elementary properties of Z-transforms

1 – Ch.5; Pg.5.1 – 4.12 LCD

38 Problems based on elementary properties of Z-transforms

1 – Ch.5; Pg.5.12 – 5.19 LCD

39 Initial and Final value theorems on Z – transforms. 1 – Ch.5; Pg.5.4 – 5.5 LCD


41 Inverse Z – transform using partial fraction 1 – Ch.5; Pg.5.26 – 5.34 LCD

42 Inverse Z – transform using residues 1 – Ch.5; Pg.5.26 – 5.34 LCD

43 Derivation of Convolution theorem. 1 – Ch.5; Pg.5.5 – 5.7 LCD

44 Inverse Z – transform using Convolution theorem. 1 – Ch.5; Pg.5.20 – 5.23 LCD

45 Tutorial class Worksheet

Continuous Assessment Test-II

46 Formation of difference equations 2 – Ch.30; Pg.1084 – 1086 LCD

47 Solution of difference equation using Z-transforms 1 – Ch.5; Pg.5.27 &

Pg.5.34 – 5.40 LCD


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




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 No *


Aids

49 Introduction to PDE and Formation of PDE by elimination of arbitrary constants and by elimination of arbitrary functions.

1 – Ch.1; Pg.1.1 – 1.21 LCD

50 Formation of PDE by elimination of arbitrary functions. 1 – Ch.1; Pg.1.1 – 1.21 LCD


52 Various solutions of a general PDE – complete, singular, particular and general integrals

1 – Ch.1; Pg.1.21 – 1.23 LCD

53 Solving standard types of PDEs of the form F(p, q) = 0 and F(z, p,q)=0.

1 – Ch.1; Pg.1.23 – 1.25 & Pg.1.28 – 1.50

LCD

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

LCD

55 Equations reducible to standard forms 1 – Ch.1; Pg.1.26 – 1.27 &

LCD


57 Solving Lagrange’s linear equation by Method of multipliers

1 – Ch.1; Pg.1.51 – 1.71 LCD


59 Solution of homogeneous linear partial differential equations of second and higher order with constant coefficients.

1 – Ch.1; Pg.1.71 – 1.98 LCD

60 Solution of non-homogeneous linear partial differential equations of second and higher order with constant coefficients.

1 – Ch.1; Pg.1.71 – 1.98 LCD

Continuous Assessment Test-III

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 Mapping CO – PO:

PO1 PO2 PO3 PO4 PO5 PO6 PO7 PO8 PO9 PO10 PO11 PO12

CO1 A

CO2

CO3 A B

CO4 A

CO5 A 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

Signature

Name Dr M RADHAKRISHNAN DR. R. MUTHUCUMARASWAMY

Designation Assistant Professor Professor & Head

Date 01.07.2015 01.07.2015

Remarks *: The same Lesson Plan may be used for MA6351 Transforms and Partial Differential Equations in the subsequent semester.

Remarks *: The same Lesson Plan(MA6351) may be followed in the subsequent semester.

* If the same lesson plan is followed in the subsequent semester/year it should be mentioned and signed by the Faculty and the HOD

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Department of Applied Mathematics - Home - Sri …€¦ · · 2015-09-09FT/GN/68/00/21.04.15 SRI VENKATESWARA COLLEGE OF ENGINEERING COURSE DELIVERY PLAN - THEORY Page 1 of 6 Department