Unit-I Introduction:
Numbers and their accuracy, Computer Arithmetic, Mathematical preliminaries, Errors and their Computation, General error formula, Error in a series approximation Solution of Algebraic and Transcendental Equation: Bisection Method, Iteration method, Method of false position, Newton-Raphson method, Methods of finding complex roots, Muller’s method, Rate of convergence of Iterative methods, Polynomial equations.
Unit-II Interpolation:
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,
Unit-III Numerical Integration and Differentiation:
Introduction, Numerical differentiation Numerical integration: Trapezoidal rule, Simpson’s 1/3 and 3/8 rule, Boole’s rule, Waddle’s rule.
Unit-IV Solution of differential Equations:
Picard’s Method, Euler’s Method, Taylor’s Method, Runge-Kutta Methods, Predictor Corrector Methods, Automatic Error Monitoring and Stability of solution
Unit-V Statistical Computation:
Frequency chart, Curve fitting by method of least squares, fitting of straight lines, polynomials, exponential curves etc, Data fitting with Cubic splines, Regression Analysis, Linear and Non linear Regression, Multiple regression, Statistical Quality Control methods.
References:
- 1. Rajaraman V, “Computer Oriented Numerical Methods”, Pearson Education
- 2. Gerald & Whealey, “Applied Numerical Analyses”, AW
- 3. Jain, Iyengar and Jain, “Numerical Methods for Scientific and Engineering Computations”, New Age Int.
- 4. Grewal B S, “Numerical methods in Engineering and Science”, Khanna Publishers, Delhi