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
identity – Harmonic Analysis. |
FOURIER TRANSFORM |
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 – Solution 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 equation
(Insulated edges excluded) – Fourier series solutions in cartesian coordinates. |
Z-TRANSFORM AND DIFFERENCE EQUATIONS |
Z-transform – Elementary properties – Inverse Z-transform – Convolution theorem –
Formation of difference equations – Solution of difference equations using Ztransform |
Text Books |
1. Grewal B.S, “Higher Engineering Mathematics”, 39th Edition, Khanna
Publishers, Delhi, 2007. |
Reference Books |
1. Bali.N.P., Manish Goyal, “A Textbook of Engineering Mathematics”, 7th
Edition, Laxmi Publications (P) Ltd.
2. Ramana.B.V. “Higher Engineering Mathematics” Tata McGraw Hill, New
Delhi
3. Glyn James, “Advanced Modern Engineering Mathematics”, 3rd Edition,
Pearson Education, 2007.
4. Erwin Kreyszig, “Advanced Engineering Mathematics” 8th Edition, Wiley
India, 2007. |