OBJECTIVES:
To enable the students to understand the mathematical concepts of special functions & complex variables and their applications in science and engineering.
OUTCOMES:
The student achieves the knowledge to analyse the problems using the methods of special functions and complex variables
Syllabus
UNIT – I:
Special Functions: Gamma and Beta Functions – their properties – Evaluation of improper integrals. Series Solutions of ordinary differential equations (Power series and Frobenius Method).
UNIT – II:
Bessel functions – Properties – Recurrence relations – Orthogonality. Legendre polynomials– Properties – Rodrigue’s formula – Recurrence relations – Orthogonality.
UNIT – III
Functions of a complex variable – Continuity – Differentiability – Analyticity – Properties – Cauchy-Riemann equations in Cartesian and polar coordinates.Harmonic and conjugate harmonic functions – Milne – Thomson method. Conformal mapping: Transformation of ez, Inz, z2, Sin z, cos z, Bilinear transformation - Translation, rotation, magnification and inversion – Fixed point – Cross ratio – Determination of bilinear transformation.
UNIT – IV
Complex integration: Line integral – Evaluation along a path and by indefinite integration – Cauchy’s integral theorem – Cauchy’s integral formula – Generalized integral formula.Complex power series: Radius of convergence – Expansion in Taylor’s series, Maclaurin’s series and Laurent series. Singular point – Isolated singular point – Pole of order m – Essential singularity.
UNIT – V
Residue – Evaluation of residue by formula and by Laurent’s series – Residue theorem. Evaluation of integrals of the type (a) Improper real integrals dxxf)
Study Material's for Mathematics-IV
Unit-I:
Frobenius Series Solution of Ordinary Differential Equations: Download
Gamma Function and Beta Function: Download
Power Method: Download
Series Solutions for Ordinary Differential Equations: Download
Unit-II:
Bessel Functions: Download
Bessel Properties: Download
Legendre Equation, Legendre Polynomial: Download
Legendre Polynomials-Formulae's: Download
Orthogonality of Bessel Functions: Download
Unit-III:Function of Complex Variable Part1: Download
Conformal Mapping: Download
Bilinear Transformation: Download
Unit-IV:
Complex Integration: Download
Isolated Singular Point: Download
Pole Of Order & Singularity: Download
Radius Of Convergence: Download
Taylor and Laurent series: Download
Taylor and Maclaurin Series: Download
Unit-V:
Improper Integral's: Download
Residue Thereom : Download
Singularities and Residues: Download
Question Papers
May/June 2017-Regular(R15): Download
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