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JNTU 2007-2008 II YEAR II SEM. B. TECH. AE - MATHEMATICS FOR AEROSPACE ENGINEERS
Posted Date: 09 Dec 2007 Resource Type: Articles/Knowledge Sharing Category: Syllabus
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Posted By: Sri Member Level: Gold
Rating:  Points: 1
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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. Bessel functions – Properties – Recurrence relations. Orthogonality of Bessel functions. Legendre functions –Legendra Polynomials- properties-recurrence relations. Orthogonality of Legendre polynomials- Rodrigue’s 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 – essential singularity
UNIT- IV
Complex power series: radius of convergence – Expansion in Taylor’s series , Maclaurins series and Laurent’s series. Residue: Evaluation of residue by formula and by Laurent series – Residue theorem –Evaluation of Integrals of type ? f(cos?, sin?) d?, ?f(x) dx ,?eimx f(x) dx; Argument principle- Rouche’s theorem – fundamental theorem of algebra. Liou ville’s 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 transformation mapping 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 elementary
theorems- conditional probability- Baye’s theorem
UNIT - VIII
Introduction to random variables – discrete and continuous- discontinuous functions. Binomial, Poisson and normal distributions and related properties, mean, standard deviation, auto and cross correlations.
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