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JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY

HYDERABAD

II Year B. Tech. AE II semester T P C

4+1* 0 4

MATHEMATICS FOR AEROSPACE ENGINEERS

UNIT -I

SPECIAL FUNCTIONS: Gamma and beta functions and their properties. Evaluation of improper integrals. Besselfunctions Properties Recurrence relations. Orthogonality of Bessel functions. Legendre functions LegendraPolynomials- properties-recurrence relations. Orthogonality of Legendre polynomials- Rodrigues formula

UNIT- II

Functions of a complex variable continuity-differentiability analyticity- properties of analytic functions.m Cauchy Riemann equations in Cartesian and polar co- ordinates .Harmonic and conjugate harmonic functions. Milne Thomson method, complex integration.

UNIT- III

Line integral evaluation along a path and by indefinite integration Cauchy integral theorem- Cauchy integral

formula. Generalized integral formula- zero- singular point- isolated singular point pole of order, m essentialsingularity

UNIT- IV

Complex power series: radius of convergence Expansion in Taylors series , Maclaurins series and Laurentsseries. Residue: Evaluation of residue by formula and by Laurent series Residue theorem Evaluation of Integralsof type ? f(cos , sin ) d , ?f(x) dx ,?e imx f(x) dx; Argument principle- Rouches theorem fundamental theorem ofalgebra. Liou villes theorem

UNIT- V:Conformal mapping, Transformation by ez , log e z z n , sinz ,cosz , z+ n/z . Bilinear transformation fixed point,cross ratio, properties, invariance of cross ratio under bilinear transformation. Determination of bilinear transformationmapping 3 given points.

UNIT- VI

Tensor analysis: Introduction to tensor analysis. Summation to convention- co variant and contravariant tensors-Fundamental and reciprocal tensors and christoffel symbols.

UNIT-VII

STATISTICS: Sample space and events probability, the axioms of probability some elementarytheorems- conditional probability- Bayes theoremUNIT - VIII

Introduction to random variables discrete and continuous- discontinuous functions. Binomial, Poisson and normaldistributions and related properties, mean, standard deviation, auto and cross correlations.

TEXT BOOKS:

1. A text book of engineering mathematics vol iv-2004 by T.K.Iyengar, B.Krishna Gandhi & Others, S.Chand andcompany.

2. Engineering Mathematics B.V.Ramana BY Tata Mc-Grawhill.

REFERENCES:1. Fundamentals of Mathematical statistics by S.C. Gupta and VK Kapoor.2. Brog .S.F. Matrix Tensor methods in Continuum Mechanics- D- VAN Nostrand company.

8/14/2019 MAE II Yr II Sem Syllabus

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