# JNTU Kakinada EEE Mathematics III Syllabus

JAWAHARLAL NEHRU TECHNOLOGICAL UNIVERSITY
II Year B.Tech EEE I-Sem T P C
4+1* 0 4
MATHEMATICS – III
UNIT – I
Special functions: Gamma and Beta Functions – Their properties – evaluation of improper integrals.
Bessel functions – properties – Recurrence relations – Orthogonality. Legendre polynomials – Properties
– Rodrigue’s formula – Recurrence relations – Orthogonality.
UNIT-II
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.
UNIT-III
Elementary functions: Exponential, trigonometric, hyperbolic functions and their properties – General
power Z C (c is complex), principal value.
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.
UNIT-V
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-VI
Residue – Evaluation of residue by formula and by Laurent series – Residue theorem.
Evaluation of integrals of the type
(a) Improper real integrals ò¥

f (x)dx (b) ò + p q q q 2 (cos ,sin ) c
c
f d
(c) ò¥

eimx f (x)dx (d) Integrals by identation.
UNIT-VII
Argument principle – Rouche’s theorem – determination of number of zeros of complex polynomials –
Maximum Modulus principle – Fundamental theorem of Algebra, Liouville’s Theorem.
UNIT-VIII
Conformal mapping: Transformation by ez , lnz, z2, z n (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 .
Text Books:
1. A text Book of Engineering Mathematics, Vol-III T. K. V. Iyengar, B. Krishna Gandhi and Others,
S. Chand & Company.
2. A text Book of Engineering Mathematics, C. Sankaraiah, V. G. S. Book Links.
3. A text Book of Engineering Mathematics, Shahnaz Bathul, Prentice Hall of India.
4. A text Book of Engineering Mathematics, P. Nageshwara Rao, Y. Narasimhulu & N. Prabhakar
Rao, Deepthi Publications.
References:
1. A text Book of Engineering Mathematics, B. V. Raman, Tata Mc Graw Hill.
2. Advanced Engineering Mathematics, Irvin Kreyszig, Wiley India Pvt. Ltd.
3. A text Book of Engineering Mathematics, Thamson Book Collection.