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### MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS MA 2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

MA2211   TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS   SYLLABUS       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 Differtial 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 equations                      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 Mathematic”, 40th Edition, Khanna publishers, Delhi, (2007)
REFERENCES
1.   Bali.N.P and Manish Goyal, “A Textbook of Engineering Mathematic”, 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

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