Numerical Methods & Computer Programming

Unit 01 : Numerical Computations, Errors and Concept of root of equation (6hrs)
A) Basic principle of numerical computation. Floating point algebra with normalized floating point
technique, Significant digits. Errors: Different types of errors, causes of occurrence and remedies to
minimize them, Generalized error formula (Derivation and Numerical )
B) Concept of roots of an equation. Descartes’ rule of signs, Intermediate value theorem, Roots of
Polynomial Equations using Birge-Vieta method.
Unit 02: Solution of Transcendental and polynomial equation and Curve Fitting: (6hrs)
A) Solution of Transcendental and polynomial equation using Bisection, Regula- Falsi, Newton-Raphson
method for single variable and two variables.
B) Curve fitting using least square approximation – First order and second order
Unit 03: Interpolation (6hrs)
Forward, Backward, Central and Divided Difference operators, Introduction to interpolation.
A)Interpolation with equal Intervals - Newton’s forward, backward interpolation formula (Derivations
and numerical), Stirling’s and Bessel’s central difference formula (Only numericals)
B) Interpolation with unequal Intervals- Newton’s divided difference formula and Lagrange’s
interpolation (Derivations and numerical).
Unit 04: Numerical Differentiation and Integration (6hrs)
A) Numerical Differentiation using Newton’s forward and backward interpolation formula (Derivation
and numerical).
B) Numerical Integration: Trapezoidal and Simpson’s rules as special cases of Newton-Cote’s
quadrature technique for single integral. Numerical on double integrals using Trapezoidal and Simpson’s
1/3 rd rule.
Unit 05:Solution of linear simultaneous equation (6hrs)
A) Solution of linear simultaneous equation: Direct methods - Gauss elimination method, concept of
pivoting – partial and complete. Gauss Jordan method, Iterative methods – Jacobi method and Gauss
Seidel method.
B)Matrix Inversion using Gauss Jordan method
Unit 06: Solution of Ordinary Differential Equation(ODE) (6hrs)
A) Solution of First order Ordinary Differential Equation (ODE) using Taylor’s series method, Euler’s
method, Modified Euler’s method (Derivation and numerical). Runge-Kutta fourth order method
(Numerical).
B)Solution of Second order ODE using 4th order Runge-Kutta method (Numerical)