Floating point Arithmetic: Representation of floating point numbers, Operations,
Normalization, Pitfalls of floating point representation, Errors in numerical computation
Iterative Methods: Zeros of a single transcendental equation and zeros of polynomial using
Bisection Method, Iteration Method, Regula-Falsi method, Newton Raphson method, Secant
method, Rate of convergence of iterative methods.
Simultaneous Linear Equations: Solutions of system of Linear equations, Gauss Elimination
direct method and pivoting, Ill Conditioned system of equations, Refinement of solution.
Gauss Seidal iterative method, Rate of Convergence.
Interpolation and approximation: Finite Differences, Difference tables, Polynomial
Interpolation: Newton’s forward and backward formula, Central Difference Formulae: Gauss
forward and backward formula, Stirling’s, Bessel’s, Everett’s formula.
Interpolation with unequal intervals: Langrange’s Interpolation, Newton Divided difference
formula, Hermite’s Interpolation, Approximation of function by Taylor’s series and Chebyshev
polynomial
Numerical Differentiation and Integration: Introduction, Numerical Differentiation, Numerical
Integration, Trapezoidal rule, Simpson’s rules, Weddle’s Rule Euler- Maclaurin Formula.
Solution of differential equations: Picard’s Method, Euler’s Method, Taylor’s Method, Runge-
Kutta methods, Predictor-corrector method, Automatic error monitoring, stability of solution.
Curve fitting and Approximation: Method of least squares, fitting of straight lines, polynomials,
exponential curves etc.