Description
Numerical and Error Analysis : Introduction, need of numerical methods, numerical analysis vs numerical methods ; Concept of exact and approximate numbers, accuracy and precision, significant digits ; Measures of Error: absolute error, relative error and percentage error; Types of error : blunder, modeling, inherent, numerical (round off, chopping and truncation) errors; Error Propagation in addition, subtraction, multiplication and division operations; Arithmetic of normalized floating point numbers and its error consequences.
Types of Equations : Linear, quadratic, higher degree polynomial equations, transcendental equations.
Non-Linear Equations : Methods to find solution of a non-linear equation : direct vs indirect method, bracketing vs open end iterative method ; Choosing initial approximation: largest possible root, search bracket, search interval; Termination criteria; Intermediate value theorem; Algorithm and methods to find roots of a non-linear equation : Bisection Method, False position method, Newton Raphson Method, BirgeVieta Method.
Simultaneous Linear Equations : Algorithm and methods to find solution of simultaneous linear equations : Direct Methods – Gauss Elimination Method, Concept of Pivoting , Gauss-Jordan Method ; Iterative Method – Gauss Seidal Method.
Interpolation : Need of interpolation, interpolation vs extrapolation ; Finite Differences – forward, backward, divided difference tables ; Methods to interpolate for given value using Newton’s Forward Difference Method, Newton’s Backward Difference Method, Newton’s Divided Difference Method and Lagrange’s Method. Concept of Inverse Interpolation
UNIT – IV
Numerical Integration : Methods and algorithm of Newton-Cotes Integration Formulae: Trapezoidal Rule, Simpson’s 1/3rd Rule, Simpson’s 3/8th Rule.
Ordinary Differential Equations : Methods and algorithm to find solution of ODEs using Euler’s Method, Runge–Kutta Methods – 2nd order & 4th order, Predictor Corrector Method – Modified Euler’s Method.
