Jntu Mathematics 3 syllabus

Jntu Mathematics 3 syllabus
MATHEMATICS III

UNIT I: Special functions I:
Review of Taylors series for a real many valued functions, Series solutions to Differential Equations. Gamma and Beta Functions Their properties evaluation of improper integrals. Bessel functions properties Recurrence relations Orthogonality.
UNIT-II Special functions II:
Legendre polynomials Properties Rodrigues formula Recurrence relations Orthogonality. Chebychers polynomials - properties 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 Thompson method.
Elementary functions: Exponential, trigonometric, hyperbolic functions and their properties General power Z (c is complex), principal value Logarithmic function.
UNIT-IV: Complex integration:
Line integral evaluation along a path and by indefinite integration Cauchys integral theorem Cauchys integral formula Generalized integral formula.
UNIT-V: Complex power series:
Radius of convergence Expansion in Taylors series, Maclaurins series and Laurent series. Singular point Isolated singular point pole of order m essential singularity.( distribution between the real analyticity and complex analyticity )
UNIT-VI: Contour integration:
Residue Evaluation of residue by formula and by Laurent series - Residue theorem.
Evaluation of integrals of the type
(a) Improper real integrals (b)
(c) (d) Integrals by identation.
UNIT-VII : Conformal mapping:
Transformation by , lnz, z2, z (n positive integer), Sin z, cos z, z + a/z. Translation, rotation, inversion and bilinear transformation fixed point cross ratio properties invariance of circles and cross ratio determination of bilinear transformation mapping 3 given points .
UNIT-VIII: Elementary Graph Theory:
Graphs, representation by matrices adjacent matrix-incident matrix- simple, multiple, regular, complete, Bipartite & Planar graphs-
Hamiltonian and Eulerian Circuits- Trees Spanning tree minimum spanning trees.
Text Books:
1. Engineering Mathematics, III by P B Bhaskara rao, SK VS RAMACHARY M Bhujanaga rao & othrs
2. A text Book of Engineering Mathematics, C. Sankaraiah, V. G. S. Book Links.
References:
1. A text Book of Engineering Mathematics, Vol-III T. K. V. Iyengar, B. Krishna Gandhi and Others, S. Chand & Company.
2. Higher engineering mathematics by b.s.grewal khanna pub
3. Adv. Eng. Maths by jain & srk iyengar, narsa publications.
4. Complex varaiables by rv Churchill
5. Adv. Eng. Maths by allen Jeffery academic press.