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 | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | |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- | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
|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 | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| | | | | |
| |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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