Computer Algorithms: Introduction, The structure of a computer, some example of Algorithms
Computer Arithmetic: Introduction, Floating point representation of numbers, Arithmetic
Operations with Normalized Floating point numbers, Consequences of Normalized Floating point,
Representation of Numbers, Some pitfalls in Computing, errors in numbers, Binary
representations of numbers, Conclusions.
Iterative Methods: Introduction, Beginning an iterative method, The method of successive
bisection, the method of false position, Newton Raphson iterative methods, The methods of
successive approximation, comparison of iterative methods, Solution of Polynomial equations,
solution of simultaneous non linear equations.
Solution of Simultaneous Algebric Equation: Introduction, The gauss elimination methods,
pivoting, illconditioned equations, Refinement of the solution obtained by Gaussian elimination,
The gauss-Seidel iterative method, An algorithms to implement the Gauss-Seidel Methods,
Comparison of direct and iterative methods.
Interpolation: Introduction, Lagrange interpolation, Difference tables, Truncation error in
interpolation, Spline Interpolation
Least squares Approximations of Functions: Introductions: Introduction, Linear Regression,
Algorithm for Linear Regression, Polynomial Regression, Fitting Exponential and Trignometric
Functions
Approximation of Functions: Introduction, Taylor Series Representation.
Differential and Integration: Introduction, Formulae for Numerical differentiation, Numerical
Integration, Simpson’s Rule, Errors in integration Formulae, Algorithm for integration of Tabulated
Function, Algorithm for integrating a known Function, Gaussian Quadrature Formulae,
Comparision of Integration Formulae.
Numerical Solution of Differential Equations: Introduction Euler’s Methods, Taylor series
Methods, Runge- Kutta Fourth order Formula, Predictor-Corrector Method, Higher Order
Differential Equation, Comparison of Predictor-Corrector and Runge- Kutta Methods.