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Mathematics -II (Numerical Methods and Complex Variables)


Answer of algebraical and Transcendental Equations: Introduction- division technique – technique of false position – Iteration technique – Newton-Raphson technique (One variable and coincident Equations).


Interpolation: Introduction- Errors in polynomial interpolation – Finite variations- Forward variations- Backward differences –Central differences – Symbolic relations and separation of symbols – variations of a polynomial-Newton’s formulae for interpolation – Interpolation with unequal intervals – Lagrange’s interpolation formula.


Numerical Integration and answer of normal Differential equations: quadrilateral rule- Simpson’s 1/3rd and 3/8th rule-Solution of normal differential equations by Taylor’s series-Picard’s technique of serial approximations-Euler’s technique – Runge-Kutta technique (second and fourth order).


Functions of a fancy variable advanced operate , Real and imagined components of advanced operate, Limit, Continuity and by-product of advanced operate, Cauchy-Riemann equations, Analytic operate, entire operate, singular purpose, conjugate operate, RC − equations in polar kind, Harmonic functions, Milne-Thomson technique, easy applications to flow issues,


Series growth and complicated Integration Line integral of a fancy operate, Cauchy’s theorem(only statement ) , Cauchy’s Integral Formula. completely oblique and uniformly oblique of series of advanced terms, Radius of convergence, Taylor’s series, Maclaurin’s series growth, Laurent’s series.


Singularities ANd Residue Theorem Zeros of an analytic operate, Singularity, Isolated singularity, Removable singularity, Essential singularity, pole of order m, easy pole, Residues, Residue theorem, Calculation of residues, Residue at a pole of order m, analysis of real definite integrals: Integration round the unit circle, Integration around semi circle, Indenting the contours having poles on the $64000 axis.

Text Books:

  1. B.S.GREWAL, Higher Engineering arithmetic, forty third Edition, Khanna Publishers. 2. N.P.Bali, Engineering arithmetic, Lakshmi Publications.
    Reference Books: one. DEAN G. DUFFY, Advanced engineering arithmetic with MATLAB, CRC Press a pair of. V.RAVINDRANATH and P.VIJAYALAKSHMI, Mathematical ways, Himalaya firm. 3. ERWIN KREYSZIG, Advanced Engineering arithmetic, tenth Edition, Wiley-India four. DAVID KINCAID, WARD CHENEY, Numerical Analysis-Mathematics of Scientific Computing, third Edition, Universities Press.