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## 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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