UNIT I:
COMPLEX ANALYSIS-I: Analytic functions, Cauchy– Riemann equations, complex integration, Cauchy’s theorem, Integral formula, Evaluation of Integrals.

UNIT II:
COMPLEX ANALYSIS-II: Singularities, poles, Residues, Residues theorem, Evaluation of real integrals of the types  ∫(0,2Π)ƒ(cosθ,sinθ) dθ, ∫(-∞,∞)e^imz ƒ(x)dx -conformal mapping – Bilinear transformations- Transformation of e^z, Z²,Sin z, and Cos z.

UNIT III:
SOLUTION OF ALGEBRAIC AND TRANSCENDENTAL EQUATIONS: The Bisection Method, The Method of False Position, Newton-Raphson Method.
INTERPOLATION: Newton’s forward and backward interpolation formula, Lagrange’s interpolation formula.

UNIT IV:
CURVE FITTING: Fitting of a straight line, Second degree curve, Exponentional curve,Power curve by method of least squares.
NUMERICAL DIFFERENTIATION AND INTEGRATION: Trapezoidal rule,Simpson’s 1/3 Rule, Simpson’s 3/8 Rule.

UNIT V:
NUMERICAL SOLUTION OF ORDINARY DIFFERENTIAL EQUATIONS: Solution by Taylor’s series, Picard’s Method of successive Approximations, Euler’s Method, RungeKutta second and fourth order methods.

TEXT BOOKS:
1. Higher Engineering Mathematics, B.S.Grewal, Khanna publishers.
2. Advanced Engineering Mathematics, Peter V.O’Neil, CENGAGE publisher.

REFERENCES:
1. Engineering Mathematics III by T.K.V. Iyengar, S.Chand publications.
2. Mathematical Methods by T.K.V. Iyengar, S.Chand publications.
3. Engineering Mathematics, Volume – III, E. Rukmangadachari & E. Keshava Reddy
Pearson Publisher.
4. Advanced Engineering Mathematics by M.C. Potter, J.L. Goldberg, Edward F.Aboufadel,and Oxford.