Engineering Mathematics-III

Taylor series method, Picard’s method, Euler’s method, Modified Euler’s method, Runge‐Kutta method. Predictor corrector methods, Adam Bashforth and Milnes method, convergence criteria, Finite difference method.

Non Linear Equations: Bisection Method, RegulaFalsi Method, Newton-Raphson Method, Iteration method. Linear Equations: Jacobi and Gauss Seidel Iteration methods, Relaxation method.

Applications of De Moivre’s theorem, Exponential, Circular, Hyperbolic and Logarithmic functions of a complex variable, Inverse Hyperbolic functions, Real and imaginary parts of Circular and Hyperbolic functions, Summation of the series-‘C+iS’ method. Limit and derivative of complex functions, Cauchy-Riemann equations, Analytic functions and its applications, Complex integration, Cauchy’s theorem, Cauchy’s integral formula, Series of complex function, Taylor series, singularities and Laurent’s series, Cauchy’s residue theorem and its application for the evaluation of real definite integrals.

Least square curve fit and trigonometric approximations, Finite differences and difference operators, Newton’s interpolation formulae, Gauss forward and backward formulae, Sterling and Bessel's formulae, Lagrange's interpolation.

Integration by trapezoidal and Simpson’s rules 1/3 and 3/8 rule, Romberg integration, and Gaussian quadrature rule, Numerical integration of function of two variables.