## MATHEMATICS lll Notes pdf (M III pdf notes)

MATHEMATICS lll Notes pdf file to download – M III pdf notes – M III notes

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UNIT – I: Special Functions I

Review of Taylor’s series fora 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-ll: Special Functions I I

Legendre polynomials -Properties – Rodrigue’s formula — Recurrence relations — Orthogonal ity. Chebycher’s polynomials — properties – recurrence relations – Orthogonality

UNIT-III

variable . Continuity – Differentiability – Analyticity – Properties – Cauchy- Riemann conditions, Maxima – Minima principle,harmonic and conjugate harmonic functions —Milne—’Thompson method. Elementary functions, general power Z‘ principal value logarithmic function.

UNIT-IV: Complex integration t I

Line integral – evaluation along a path and by indefinite integration – Cauchy’s integral theorem — Cauchy’s integral formula – Generalized integral formula.

UNIT-V: Complex power series a

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. (Distinction 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 ∫f(x) [-∞ +∞] (b) ∫f(cos x, sin x)dx (c) ∫eimxf(x)dx (d) Integrals by indentation.

UNIT-VII: Conformal mapping C

Transformation by e, Imz, z2. zn (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 transfonnation mapping 3 given points

UNIT -VIII: Elementary Graph theory

Graphs, Representation by manices Adjacent matrix – Incident matrix -Simple, Multiple, Regular . complete , Bipartite & Planar graphs – . Hamiltonian and Eulerian Circuits- Trees Spanning tree -minimum

#### TEXT BOOKS: [ M III pdf notes | MATHEMATICS lll Notes Pdf | MATHEMATICS lll Notes | M III notes | M III pdf ]

1.Engineering Mathematics III by PB Bhaskar Rao, SKVS Ramana Chary and others.

2.Engineering Mathematics III by C Shankaraiah VGS Book links.

#### REFERENCES: [ M-III pdf notes | MATHEMATICS — lll Notes Pdf | MATHEMATICS — lll Notes | M-III notes | M-III pdf ]

I. Engineering Mathematics –HI by T.K.V. Iyengar, B.Krishna Gandhi and Others — S.Chand. g C . .

2. Higher Engineering Mathematics by B.S. Grewal Khanna Publications. i W

3. Agtyanceﬁngineering Mathematics by Jain & S.R.K. Iyengar, r Narasa Publications.

4. ” Complex Yariables by R.V. Churchill.