FIFTH SEMESTER MATHEMATICS
Numerical Methods 6A
Unit – 1: Finite Differences and Interpolation with Equal intervals
1. Introduction, Forward differences, Backward differences, Central Differences, Symbolic relations, nth Differences of Some functions,
2. Advancing Difference formula, Differences of Factorial Polynomial, Summation of Series.
3. Newton’s formulae for interpolation. Central Difference Interpolation Formulae.
Unit – 2: Interpolation with Equal and Unequal intervals
1. Gauss’s Forward interpolation formulae, Gauss’s backward interpolation formulae, Stirling’s formula, Bessel’s formula.
2. Interpolation with unevenly spaced points, divided differences and properties, Newton’s divided differences formula.
3. Lagrange’s interpolation formula, Lagrange’s Inverse interpolation formula.
Unit – 3: Numerical Differentiation
1. Derivatives using Newton’s forward difference formula, Newton’s back ward difference formula,
2. Derivatives using central difference formula, Stirling’s interpolation formula,
3. Newton’s divided difference formula, Maximum and minimum values of a tabulated function.
Unit – 4: Numerical Integration
1. General quadrature formula one errors, Trapezoidal rule,
2. Simpson’s 1/3– rule, Simpson’s 3/8 – rule, and Weddle’s rules,
3. Euler – McLaurin Formula of summation and quadrature, The Euler transformation.
Unit – 5: Numerical solution of ordinary differential equations
1. Introduction, Solution by Taylor’s Series,
2. Picard’s method of successive approximations,
3. Euler’s method, Modified Euler’s method, Runge – Kutta methods.