MA 2211-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. |
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. |
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 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). |