MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS
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
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
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
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
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
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 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 (2007).
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