BSc IT‎ > ‎FYBSc IT‎ > ‎

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



Comments