|
UNIT I |
FOURIER SERIES |
12 |
|
Dirichllet`s conditions-
General Fourier Series- Odd and Even functions - Half range Fourier Series-
Parseval`s identity- Harmonic. |
|
UNIT II |
COMPLEX DIFFERENTIATION |
12 |
|
Function of a complex variable-
Analytic Function - Necessary conditions Cauchy Riemann equations-sufficient
conditions (excluding proof) - Properties of analytic functions - Harmonic
conjugate - Construction of analytics functions-( Milne-Thomson`s method) -
Conformal mappings: Mappings w=z+a, az, 1/z,
z + 1/z and bilinear transformation.
|
|
UNIT III |
COMPLEX INTEGRATION |
12
|
|
Statement and application of
Cauchy`s integral theorem (without proof)
and Cauchy`s integral formulae (without proof) -Taylor`s and Laurent`s
expansions - Singularities -Poles and Residues - Cauchy`s residue theorem
(with proof) - Contour integration - integration around unit circle |
|
UNIT IV |
LAPLACE TRANSFORMS |
12 |
|
Laplace
transforms-Conditions for existence -Transforms of simple functions - Basic
properties - Derivatives and integrals of transforms-Transforms of
derivatives and integrals - Initial and final value theorems-transforms of
unit step function and unit impulse function -transform of periodic functions
|
|
UNIT V |
INVERSE LAPLACE
TRANSFORMS |
12 |
|
Inverse Laplace
transforms - Convolution theorem -Solution of linear ordinary differential
equations of second order with
constant coefficients.
TOTAL: 60+15 |
|
TEXT BOOKS: |
|
Sl. No. |
Author(s) |
Title of the Book |
Publisher |
Year of
Publication |
|
1. |
Kandasamy P,
Thilagavathy K and
Gunavathy K |
Engineering Mathematics |
S Chand and Co ,New Delhi |
2010 |
|
2. |
Veerarajan T |
Engineering Mathematics |
Tata McGraw Hill Publishing
Co. |
2005
|
|
3. |
Kandasamy P Thilagavathy K and
Gunavathy K |
Engineering Mathematics- Volume-III |
S Chand and Co New Delhi |
1996 |
|
REFERENCE BOOKS: |
|
Sl. No. |
Author(s) |
Title of the Book |
Publisher |
Year of
Publication |
|
1. |
Kreyszig E |
Advanced Engineering Mathematics |
John Wiley and Sons, Singapore |
2001 |
|
2. |
Grewal B S |
Higher Engineering Mathematics |
Khanna Publishers |
2004 |
|
3. |
Venkataraman M K |
Engineering Mathematics |
National Publishing Co.,
Chennai. |
2000 |
|
4. |
Narayanan S Manicavachagom
Pillay T and K Ramanaiah G |
Advanced Mathematics for engineering students |
S
Viswanathan Printers and Publishers |
1992 |
|
WEB URLs:
- www.mathworld.wolfram.com
- www.answers.com/topic/differential-equation
- www.math.fullerton.edu/mathews/c2003/ComplexIntegralMod.html
- www.cs.uiuc.edu/homes/lukeo/2003fall/AM33/files/laplace.pdf
- www.physics.miami.edu/~nearing/mathmethods/vector_calculus-2
|
