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### 181301 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATION SYLLABUS ANNA UNIVERSITY CHENNAI 2010 REGULATION

181301 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS 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”, 40
th
Edition, Khanna publishers,
Delhi, (2007)
REFERENCES
1. Bali.N.P and Manish Goyal, “A Textbook of Engineering Mathematic”, 7
th
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”, 3
rd
Edition, Pearson
Education (2007).
4. Erwin Kreyszig, “Advanced Engineering Mathematics”, 8
th
edition, Wiley India
(2007).3