|
Course
Code :: MA1202 |
(L-T-P) :: 2+4+0 |
Credits
:: 4 |
Laplace Transform: Definition of Laplace Transform,
linearity property,
conditions for existence of Laplace Transform. First and second
shifting
properties, Laplace Transform of derivatives and integrals, unit
step
functions, Dirac delta-function, error function. Differentiation
and
integration of transforms, convolution theorem, inversion,
periodic functions.
Evaluation of integrals by Laplace Transform. Solution of
initial and boundary
value problems.
Fourier Series : Periodic functions, Fourier series
representation of a
function, half range series, sine and cosine series, Fourier
integral formula,
Parseval's identity.
Fourier Transform: Fourier Transform, Fourier sine
and cosine transforms.
Linearity, scaling, frequency shifting and time shifting
properties. Self reciprocity
of Fourier Transform, convolution theorem. Applications to
boundary value
problems. Brief Introduction of Z-Transform, Mellin transform
and Wavelet
Transform.
Text Books:
1.
Jain.
R.K. Iyengar. S.R.K., Advanced Engineering Mathematics, 3rd
Edition, Narosa.
2.
Churchill.
R.V. Brown. J.W., Fourier series and boundary value problems, Mc
Graw. Hill.
Reference Books:
1.
E. Kreyszig
Advanced Engineering
Mathematics, 9th Edition, John Wiley & Sons (1999)
2.
H.Dym and
H.P Mc Kean, Fourier
series and integrals, Academic press, Newyork (1972)