LESSON PLAN

Faculty Name : D.SAMUNDEESWARI

Sub Code : MA2211

Sub Name : Transforms & PDE

Academic Period : JULY- 12 to DEC -12

Branch: II MECH ‘A’

Year : II

Semester : III

Date of

Compilation :

SYLLABUSMA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATION 3 1 0 4

(Common to all branches) OBJECTIVES The course objective is to develop the skills of the students in the areas of Transforms and Partial Differential Equations. This will be necessary for their effective studies in a large number of engineering subjects like heat conduction, communication systems, electro-optics and electromagnetic theory. The course will also serve as a prerequisite for post graduate and specialized studies and research. 1. FOURIER SERIES 9 + 3

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.2. FOURIER TRANSFORMS 9 + 3

Fourier integral theorem (without proof) – Fourier transform pair – Sine and Cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.3. PARTIAL DIFFERENTIAL EQUATIONS 9 + 3

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.4. APPLICATIONS OF PARTIAL DIFFERENTIAL EQUATION 9 + 3

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. 5. Z -TRANSFORMS AND DIFFERENCE EQUATIONS 9 + 3 Z-transforms - Elementary properties – Inverse Z-transform – Convolution theorem -Formation of difference equations – Solution of difference equations using Z-transform.

Lectures : 45 Tutorials : 15 Total : 60

TEXT BOOKS

1. Grewal, B.S, “Higher Engineering Mathematics”, 40th Edition, Khanna publishers, Delhi, (2007)

REFERENCES

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

Edition,       Laxmi Publications(P) Ltd. (2007)2. Ramana.B.V., “Higher Engineering Mathematics”, Tata Mc-GrawHill Publishing Company

limited, New Delhi (2007).3. Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition, Pearson

Education (2007).4. Erwin Kreyszig, “Advanced Engineering Mathematics”, 8th edition, Wiley India (2007).

OTHER REFERENCES

1. T.Veerarajan, Engineering Mathematics-III, Tata McGraw Hill.

Sl.No. TOPICS

No. of Hours

BookProposed

dateRev- I Rev- II Rev- III Actual

dateRemark

UNIT I 11+3

1 Fourier Series – Dirichlet’s conditions

1 O1

2 General Fourier series in (0,2π) 1 O13 Fourier series in (-π,π) 1 O14 Tutorial 15 Fourier series in (0,2l) 1 O16 Fourier series in (-l,l) 1 O17 Half range Cosine series 1 O18 Half Range Sine series 1 O19 Tutorial 110 Complex form of Fourier series 1 O111 Parseval’s Identity 1 O112 Harmonic Analysis 1 O113 Harmonic Analysis 1 O114 Tutorial 1

UNIT II 9+3

15 Fourier Integral Theorem 1 O116 Fourier Sine & Cosine Integrals 1 O117 Fourier Transform Pair 1 O118 Tutorial 119 Properties 1 O120 Fourier Cosine Transforms 1 O121 Fourier Sine Transforms 1 O122 Tutorial 1

23 Properties of sine and Cosine Transforms

1 O1

24 Convolution Theorem 1 O125 Parseval’s Identity 1 O126 Tutorial 1

UNIT III 11+3

27Formation of PDE by elimination of arbitrary Constants

1 O1

28 Formation of PDE by elimination of arbitrary functions

1 O1

29

Solutions of std. types of 1st order PDEEquations of type f(p.q)=0, z=px+qy+f(p,q)

1 O1

30 f(x,p.q)=0, f(y,p.q)=0 1 O131 Tutorial 132 f(z,p.q)=0, Separable equations 1 O1

33 f(xmp, ynq)=0 1 O134 f(z, xmp, ynq)=0 1 O135 Tutorial 1

36Lagrange’s Linear EquationMethod of Grouping

1 O1

37 Method of multipliers 1 O1

38Linear PDE’s of Second and Higher order with constant coefficients

1 O1

39Linear PDE’s of Second and Higher order with constant coefficients

1 O1

40 Tutorial 1

UNIT IV 11+2

41 Solutions of One – Dimensional Wave equation

1 O1

42 Vibrating String with Zero initial velocity

1 O1

43 vibrating string with zero initial velocity

1 O1

44 Tutorial 1

45 Vibrating String with Non Zero initial velocity

1 O1

46 Vibrating String with Non Zero initial velocity

1 O1

47 Tutorial

48 One – Dimensional Heat Flow-Equations

1 O1

49 One – Dimensional Heat Equations with zero boundaries

1 O1

50 One – Dimensional Heat Equations with zero boundaries

1 O1

51 Steady State Heat Flow - Problems

1 O1

52 Two Dimensional Heat Equations

1 O1

53 Tutorial 1

UNIT V10+3

54 Definition Z –Transforms 1 O155 Some Standard Z –Transforms 1 O156 Properties Z –Transforms 1 O157 Tutorial 158 Initial and Final Value Theorem 1 O159 Initial and Final Value Theorem 1 O160 Inverse Z – transform 1 O161 Inverse Z – transform 1 O162 Tutorial 163 Convolution Theorem 1 O1

64 Formation of Difference equations

1 O1

65 Solution of Difference equations using Z -Transform

1 O1

66 Tutorial 1TOTAL 66

FACULTY INCHARGE HOD PRINCIPAL