SEMESTER II COURSE : S.BIT.2.02
[Total Lectures 75]
APPLIED MATHEMATICS II
To study advanced mathematical concepts used in software development of Computer Graphics, animation, image processing, cryptography, etc.
UNIT 1. Complex Numbers: 
Cartesian, Polar & Exponential form, De-Moivre's theorem, Hyperbolic functions, Logarithms of Complex numbers
UNIT 2. Complex Variables : 
Cauchy Riemann Equations, , Conformal Mapping and Bilinear Mapping, concept of Line Integral, Riemann Integral, Singularities –Poles, Evaluation of Residues theorem.
UNIT 3. Laplace 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 4. 
Differentiation under Integral sign, Beta and Gamma Functions, Properties and Duplication Formula, Error Functions
UNIT 5. 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 6. Integral Calculus: 
Double Integral, Area, Triple Integral, Volume Continuous Internal Assessment Assignments / Project Mid Term test.
1. Engineering Mathematics A tutorial approach by R. R. Singh and Mukul Bhatt,
2. Differential Calculus by Shanti Narayan.
3. B. S. Grewal, “Higher Engineering Mathematics.
4. Advanced Engineering Mathematics: R.K.Jain, S.R.K. Iyengar, Narosa Publishing
5. Engineering Mathematics : T Veerajan, Tata McGraw-Hill
6. Integral Transforms: A. R. Vasishta, Dr. R.K. Gupta, Krishna Prakashan Mandir