MA2211-Transforms and Partial Differential Equations |
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. |
FOURIER TRANSFORMS |
Fourier integral theorem (without proof) – Fourier transform pair – Sine and
Cosine transforms – Properties – Transforms of simple functions – Convolution theorem – Parseval’s identity.
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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. |
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 |
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.
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REFERENCE |
Text Books |
1.Grewal, B.S, ‘Higher Engineering Mathematics’ 40th Edition, Khanna publishers, Delhi,(2007). |
Reference Books |
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). |