## Mathematics -II (Numerical Methods and Complex Variables)

**UNIT I: **

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

**UNIT II:**

**Interpolation:** Introduction- Errors in polynomial interpolation â€“ Finite variations- Forward variations- Backward differences â€“Central differences â€“ Symbolic relations and separation of symbols – variations of a polynomial-Newtonâ€™s formulae for interpolation â€“ Interpolation with unequal intervals – Lagrangeâ€™s interpolation formula.

#### UNIT III:

Numerical Integration and answer of normal Differential equations: quadrilateral rule- Simpsonâ€™s 1/3rd and 3/8th rule-Solution of normal differential equations by Taylorâ€™s series-Picardâ€™s technique of serial approximations-Eulerâ€™s technique – Runge-Kutta technique (second and fourth order).

#### Unit-IV:

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 âˆ’ equations in polar kind, Harmonic functions, Milne-Thomson technique, easy applications to flow issues,

#### Unit-V:

Series growth and complicated Integration Line integral of a fancy operate, Cauchyâ€™s theorem(only statement ) , Cauchyâ€™s Integral Formula. completely oblique and uniformly oblique of series of advanced terms, Radius of convergence, Taylorâ€™s series, Maclaurinâ€™s series growth, Laurentâ€™s series.

#### Unit-VI:

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:

- 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.

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