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### SEMESTER II

 SEMESTER II COURSE : S.BIT.2.02 [Total Lectures 75] APPLIED MATHEMATICS II LEARNING OBJECTIVE: To study advanced mathematical concepts used in software development of Computer Graphics, animation, image processing, cryptography, etc. UNIT 1. Complex Numbers:                                                                [13] Cartesian, Polar & Exponential form, De-Moivre's theorem, Hyperbolic functions, Logarithms of Complex numbers UNIT 2. Complex Variables :                                                               [13] Cauchy Riemann Equations, , Conformal Mapping and Bilinear Mapping, concept of Line Integral, Riemann Integral, Singularities –Poles, Evaluation of Residues theorem. UNIT 3. Laplace Transform:                                                                [13] 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.                                                                                                      [12] Differentiation under Integral sign, Beta and Gamma Functions, Properties and Duplication Formula, Error Functions UNIT 5. Fourier Series:                                                                          [12] 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:                                                                      [12] Double Integral, Area, Triple Integral, Volume Continuous Internal Assessment Assignments / Project Mid Term test. REFERENCES: 1. Engineering Mathematics A tutorial approach by R. R. Singh and Mukul Bhatt, TMH 2010 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 House. 5. Engineering Mathematics : T Veerajan, Tata McGraw-Hill 6. Integral Transforms: A. R. Vasishta, Dr. R.K. Gupta, Krishna Prakashan Mandir