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Mar 7, 2012

MA2161 Mathematics II - SUBJECT CATALOG

SUBJECT RESOURCES:

CLICK HERE to access 'Question Banks'


CLICK HERE to access 'Previous Year Question Papers'


CLICK HERE to access 'Important Formulas'


CLICK HERE to search more about this subject



SYLLABUS:



MA2161          MATHEMATICS II                                                                                        L T P C
3 1 0 4


UNIT I ORDINARY DIFFERENTIAL EQUATIONS            12
Higher order linear differential equations with constant coefficients Method of variation of parameters – Cauchys and Legendres linear equations Simultaneous first order linear equations with constant coefficients.

UNIT II            VECTOR CALCULUS           12
Gradient Divergence and Curl Directional derivative Irrotational and solenoidal vector fields Vector integration Greens theorem in a plane, Gauss divergence theorem and stokes’ theorem (excluding proofs) Simple applications involving cubes and rectangular parallelpipeds.

UNIT III           ANALYTIC FUNCTIONS      12
Functions of a complex variable Analytic functions Necessary conditions, Cauchy Riemann equation  and  Sufficient  conditions  (excluding  proofs)   Harmonic  anorthogonal  properties of analytic function Harmonic conjugate Construction of analytic functions Conformal mapping : w= z+c, cz, 1/z, and bilinear transformation.


UNIT IV           COMPLEX INTEGRATIO12
Complex  integration  Statement  and applications of  Cauchys  integratheorem and  Cauchys integral formula Taylor and Laurent expansions Singular points Residues Residue theorem Application of residue theorem to evaluate real integrals Unit circle and semi-circular contour(excluding poles on boundaries).

UNIT V            LAPLACE TRANSFORM     12
Laplace transform Conditions for existence Transform of elementary functions Basic properties
Transform of derivatives and integrals Transform of unit step function and impulse functions
Transform of periodic functions.
Definition of Inverse Laplace transform as contour integral Convolution theorem (excluding proof) Initial and Final value theorems Solution of linear ODE of second order with constant coefficients using Laplace transformation techniques.
TOTAL : 60 PERIODS



TEXT BOOK:
rd
1.  Bali  N.  P  and  Manish  Goyal,  Text  book  of  Engineering  Mathematics,  3
Publications (p) Ltd., (2008).


Edition,  Laxmi
th
2.  Grewal. B.S, “Higher Engineering Mathematics, 40
Edition, Khanna Publications, Delhi, (2007).

REFERENCES:
1.  Ramana  B.V,  “Higher  Engineering  Mathematics,Tata  McGraw  Hill  Publishing  Company, New Delhi, (2007).
rd
2.  Glyn James, Advanced Engineering Mathematics, 3
Edition, Pearson Education, (2007).
th
3.  Erwin Kreyszig, Advanced Engineering Mathematics, 7
Edition, Wiley India, (2007).
rd
4.  Jain  R.K  and  Iyengar  S.R.K,  Advanced  Engineering  Mathematics,  3
Publishing House Pvt. Ltd., (2007).
Edition,  Narosa

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