MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

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MA2211 TRANSFORMS AND PARTIAL DIFFERENTIAL EQUATIONS

How to study this subject

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.
TOTAL (L:45+T:15): 60 PERIODS
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”, 8
th
 edition, Wiley India (2007).


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