Transforms and Partial differential Equations Syllabus(Maths III)

For Further Reading, Anna university third semester syllabus, engineering, Third Semester syllabus

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MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS                                                                                         L T P C

(Common to all branches)                                                                                  3 1 0 4

OBJECTIVE:
        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.


UNIT I FOURIER SERIES 9 
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 
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 
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 
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 
Z-transforms - Elementary properties – Inverse Z-transform – Convolution theorem -
Formation of difference equations – Solution of difference equations using Z-transform.


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’, 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).

For Further Reading,

Anna university third semester syllabus, engineering, Third Semester syllabus