Numbers and Errors

Significant figures, Absolute and relative error, Rounding error in functional evaluation, Propagation of error in arithmetic process and Truncation errors (Taylor’s series).

Single Non-linear Equation

Method of iteration, Bisection method, False position method, Secant method, Fixed point method, Newton Raphson method convergence.

Interpolation

Difference tables, Newton forward and backward interpolation formula with error, Divided difference and central difference formula, Lagrange’s interpolation formula, Curve fitting by least squares, Cubic spline, Chebyshev polynomials and Min- max properties.

Solution of Systems of Linear Equations

Gaussian elimination, Gauss elimination with pivoting, Gauss-Jordan method.

Numerical Differentiation and (Numerical) Integration

Trapezoidal rule, Simpson’s rule, Romberg rule with error and Weddle’s method.

Solution of Differential Equations

Modified Euler method, Euler’s method, Picard’s method, Runge–Kutta method, Predictor corrector method, Linear algebraic systems, Direct and iterative methods, Matrix inversion.

Solution of Partial Differential Equations

Introduction to partial differential equation, Geometric interpretation, Elliptic, Parabolic and hyperbolic partial differential equation.

Least Squares Approximation of Functions

Linear and polynomial regression, Fitting exponential and Trigonometric functions.