TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS Syllabus

MA2211  TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS             L T  P C
 (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.

UNIT I     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.


UNIT II     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.

UNIT III     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.

UNIT IV     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.

UNIT V     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.



TEXT BOOKS

TOTAL: 60 PERIODS

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’, Seventh 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’,  Third  edition-Pearson
Education (2007).
4.  Erwin  Kreyszig  ’Advanced  Engineering  Mathematics’,  Eighth  edition-Wiley  India
(2007).