NOTE: Attempt any FIVE questions selecting at least TWO questions from each section.

Section-I (5/9)

Error Analysis

•    Errors, Absolute errors, Rounding errors, Truncation errors

•    Inherent Errors, Major and Minor approximations in numbers

The Solution of Linear Systems 

•    Gaussian elimination method with pivoting, LU Decomposition methods, Algorithm and convergence of Jacobi iterative Method, Algorithm and convergence of Gauss Seidel Method

•    Eigenvalue and eigenvector, Power method

The Solution of Non-Linear Equation

•    Bisection Method, Fixed point iterative method, Newton Raphson method, Secant

method, Method of false position, Algorithms and convergence of these methods

Difference Operators

•    Shift operators

•    Forward difference operators

•    Backward difference operators

•    Average and central difference operators

Ordinary Differential Equations

•    Euler’s, Improved Euler’s, Modified Euler’s methods with error analysis

•    Runge-Kutta methods with error analysis

•    Predictor-corrector methods for solving initial value problems

•    Finite Difference, Collocation and variational methods for boundary value problems



Section-II (4/9)

Interpolation

•    Lagrange’s  interpolation

•    Newton’s divided difference interpolation

•    Newton’s forward and backward difference interpolation,  Central difference interpolation 

•    Hermit interpolation

•    Spline interpolation

•    Errors and algorithms of these interpolations

Numerical Differentiation

•    Newton’s Forward, Backward and central formulae for numerical differentiation

Numerical Integration

•    Rectangular rule

•    Trapezoidal rule

•    Simpson rule

•    Boole’s rule

•    Weddle’s rule

•    Gaussian quadrature formulae

•    Errors in quadrature formulae

•    Newton-Cotes formulae

Difference Equations

•    Linear homogeneous and non-homogeneous difference equations with constant coefficients