SUBJECT DESCRIPTION AND OBJECTIVES



SARDAR RAJA COLLEGE OF ENGINEERING

RAJA NAGAR, ALANGULAM

Department of Electronics and Communication Engineering

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Subject Name : TRANSFORMS & PDE

Subject Code : MA 2211

Year/Branch : II – BE / ECE

Semester : III

Prepared By,

Ms.T.Mariselvi

Asst. Prof/Mathematics

Humanities and Science Department

SUBJECT DESCRIPTION AND OBJECTIVES

AIM:

This subject deals with the topics Fourier Series, Fourier Transform, Z-Transforms, Partial Differential Eqns & Boundary Value problems.

OBJECTIVES:

The topics of this paper was chosen in such a way that this will help the engineering students for effective understanding of Engineering subjects and also gives a foundation for solving engineering subjects problem in higher semester.

UNIVERSITY TEXT BOOK :

1. Higher Engineering Mathematics by Mr.B.S.Grewal

COLLEGE REFERED BOOK :

1.Transforms and Partial Differential Equations by G. Balaji

2.Transforms and Partial Differential Equations-Dr.A.Singaravelu

3.Engineering Mathematics III by Mr. P. Kandasamy,K.Thilagavathy and

K. Gunavathy

REFERENCES:

1. Integral Transforms for Engineers and Applied Mathematicians by

Andrews L.A and Shiva Moggi B.K.

2. Advance Maths for Engineering Students – Volume II & III by

Narayanan.S, Manicavachagom Pillay. T.K & Raman iah.G

MICRO LESSON PLAN

|WEEK |HOURS |LECTURE TOPIC |READING | |

| | | | | |

| | | | |ASSIGNMENT |

| | | | | |

|I,II |1-5 |UNIT II- FOURIER TRANSFORM |Text book 2 | |

|III | |Fourier intergral theorem (without proof). |(2.1-2.7) | |

| | |Fourier Transform & Inverse Transform | | |

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| | | | |A 1 |

| | | | | |

| |6-7 |Fourier Transform of unit step and Dirac Delta function |Text book 2 | |

| | | |(2.9-2.39) | |

| |8-10 | Fourier transform pair-Sine and Cosine Properties - Transform of Simple |Text book 2 | |

| | |functions |(2.42-2.78) | |

| |11-12 |Convolutions theorem –Parseval’s identity & Complex Form |Text book 2 | |

| | | |(2.79-2.93) | |

|IV ,V |13-17 |UNIT V-Z-TRANSFORM AND DIFF EQUNS. |Text book 2 |A2 |

| | |Z-Transform- Elementary properties –Inverse Z-transform |(5.2-5.76) | |

| |18-19 |Solution of difference equations using Z-transform |Text book 2 | |

| | | |(5.77-5.92) | |

| |20-24 |Convolution theorem – Formation of difference equations |Text book 2 | |

| | | |(5.98-5.105) | |

| |25-28 |UNIT-III PARTIAL DIFFERENTIAL EQUATIONS |Text book 2 | |

| | |Order degree of PDE, Formation of Partial differential equations by |(3.1-3.41) | |

| | |elimination of arbitrary constants and arbitrary functions- | | |

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|VI, | | | | |

|VII | | | | |

| |29-30 | | |A3 |

| | |Soln of standard types of first order PDE |Text book 2 | |

| | | |(3.48-3.104) | |

| |31-33 |Lagrange’s linear eqn |Text book 2 | |

| | | |(3.105-3.127) | |

| |34-36 |Linear PDE of second and higher order with constant coefficients. |Text book 2 | |

| | | |(3.129-3.163) | |

| | | | | |

|WEEK |HOURS |LECTURE TOPIC |READING | |

| | | | | |

| | | | |ASSIGNMENT |

|VIII,IX |37-39 |UNIT I -FOURIER SERIES |Text book 2 | |

| | |Introduction to Periodic Function, Dirichlets conditions-General Fourier |(1.1-1.38) | |

| | |Series | | |

| |40-42 | Odd and Even functions |Text book 2 | |

| | |Half range sine series and cosine series |(1.39-1.165) | |

| |43-45 |Complex form of Fourier Series –Parseval’s identify – RMS value |Text book 2 | |

| | | |(1.169-1.93) | |

| |46-48 |Harmonic Analysis RMS value -Harmonic Analysis |Text book 2 |A5 |

| | | |(1.195-1.208) | |

| |49-50 |UNIT IV- APPLICATIONS OF PDE |Text book 2 | |

| | |Classification of second order quasi-linear partial differential equations |(4.2-4.14) | |

| |51-56 |Transverse Vibration of stretched elastic String-Solutions of one |Text book 2 | |

| | |dimensional heat equation and wave equation |(4.15-4.85) | |

|X,XI | | | | |

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| |57-59 |Steady state solution of two- dimensional equation of heat condition |Text book 2 | |

| | |(insulated edges excluded) |(4.87-4.147) | |

| |60 |Fourier series solution in Cartesian coordinates | Text book 2 | |

| | | |(4.149-4.161) | |

QUESTION BANK

UNIT I- FOURIER SERIES

PART A

1. State Dirichlet’s condition for a function to be expanded as a Fourier series.

2. Find the Fourier constants bn for xsinx in (-(, ()

3. State the Parseval’s identity for the half-range cosine expansion of f(x) in (0, 1).

4. State Dirichlets condition for a function to be expanded as a fourier series

5. Find the constant a0 of the Fourier series for function f(x) = x in 0 ( x ( ((.

6. Find bn in the expansion of x2 as a Fourier series in (-((().

7. Write the Fourier sine series of k in (0(().

8. Write parseval’s theorem on Fourier constants.

9. Define root mean square value of a function.

10. If f(x) = x2 in (( ( x ( (.find the RMS value of f(x) is (4/5 say true or false.

11. Find the cosine series for f(x) = 1, 0 ( x ( a((.

-1, a/2 < x < a.

12. Find the RMS value of the function f(x) = x in (0, 1).

13. If f(x) = |x| expanded as a Fourier series in -( < x < (. Find a0.

14. Is a function f(x) = 1+2x/(, -( < x < 0.

1-2x/(, 0 < x < (. Is odd . say true or false.

15. Find the constant a0 of the Fourier series for the function f(x) = x cos x , -( < x < (

PART B

1.(i)Find the Fourier series expansion of a periodic function f(x) of period 2l defined by

f(x) = l+x , -l ................
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