Unit – IComplex Numbers: Cartesian, Polar & Exponential form, De-Moivre’s theorem, Hyperbolic functions, Logarithms of Complex numbers
Unit – IIComplex Variables : Cauchy Riemann Equations, , Conformal Mapping and Bilinear Mapping, concept of Line Integral, Riemann Integral, Singularities –Poles, Evaluation of Residues theorem.
Unit – IIILaplace Transform: Introduction, Definition, Properties of Laplace Transform, Laplace Transform of standard function.

Inverse Laplace Transform:

Inverse Laplace Transform , Methods of obtaining Inverse Laplace transform, Laplace transform of Periodic Functions, Heavyside Unit-step Function, Dirac-delta function (Unit Impulse Function), Application of Inverse Laplace transform to solve differential equations.

Unit – IV

Differentiation under Integral sign, Beta and Gamma Functions,

Properties and Duplication Formula, Error Functions

Unit – V

Fourier Series:

Fourier Series, Change of Interval, Even and odd functions, Half range expansions.

Fourier Transform and Inverse Fourier Transform: 

Fourier transform of Even and Odd functions, Fourier Transform of sine and cosine functions

Unit – VI

Integral Calculus: Double Integral, Area, Triple Integral, Volume
Problem Solving
List of Problems

 

i) Problem solving based on Complex Numbers ii)Problem solving based on Complex Variables iii) Problem solving based on Laplace Transforms iv) Problem solving based on Inverse Laplace Transforms

v) Problem solving based on Differentiation under the integral sign vi) Problem solving based on Beta and gamma functions vii)Problem solving based on error functions viii) Problem solving based on Fourier series ix) Problem solving based on Fourier transforms

x) Problem solving based on double integrals and area xi)Problem solving based on triple integrals

 

References:

Differential Calculus by Shanti Narayan.

B. S. Grewal, “Higher Engineering Mathematics.

Advanced Engineering Mathematics:  R.K.Jain, S.R.K.  Iyengar, Narosa Publishing House.

Engineering Mathematics : T Veerajan, Tata McGraw-Hill

Integral Transforms:  A. R. Vasishta, Dr. R.K. Gupta, Krishna Prakashan Mandir.

Download ebook – Applied Mathematics – 2 [PDF]