November 30, 2012

Applied Mathematics - 2

Portion and Syllabus of Applied Mathematics -2 of Semester 2 of F.Y.B.Sc.(I.T.) is as follows:
  • Complex Nimbers
    • Cartesian
    • Polar & Exponential form
    • De Moivre's Theorem
    • Hyperbolic Functions
    • Logarithms of Complex Numbers
  • Complex Variables
    • Cauchy Riemann Equations
    • Conformal Mapping and Bilinear Mapping
    • Concept of Line Integral
    • Reimann Integral
    • Singularities - Poles, Evaluation of Residues Theorem
  • 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.
  • Differentiation under Integral sign
  • Beta and Gamma functions
  • Properties and Duplication Formula
  • Error Functions
  • Fourier Series
    • Fourier Series
    • Change of Interval
    • Even and Odd function
    • Half range expansions
    • Fourier Transform and Inverse Fourier Transform
    • Fourier Transform of Even and Odd functions
    • Fourier Transform of Sine and Cosine functions
  • Integral Calculus
    • Double Integral
    • Area
    • Triple Integral
    • Volume
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.


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