ANTC (B-TECH Mechanical Engineering 5th)

UNIT – I ERRORS IN NUMERICAL CALCULATIONS

Introduction, Numbers and their accuracy, Absolute, relative and percentage errors and their analysis,

General error formula.

UNIT – II INTERPOLATION AND CURVE FITTING

Taylor series and calculation of functions, Introduction to interpolation, Lagrange approximation, Newton

Polynomials, Chebyshev Polynomials, Least squares line, curve fitting, Interpolation by spline functions.

UNIT – III NUMERICAL DIFFERENTIATION AND INTEGRATION

Approximating the derivative, Numerical differentiation formulas, Introduction to Numerical quadrature,

Newton-Cotes formula, Gaussion Quadrature.

UNIT – IV SOLUTION OF NONLINEAR EQUATIONS

Bracketing methods for locating a root, Initial approximations and convergence criteria, Newton- Raphson

and Secant methods, Solution of problems through a structural programming language such as C or Pascal.

UNIT – V SOLUTION OF LINEAR SYSTEMS

Direct Methods, Gaussian elimination and pivoting, Matrix inversion, UV factorization, Iterative methods

for linear systems, Solution of problems through a structured programming language such as C or Pascal.

UNIT – VI EIGEN VALUE PROBLEMS

Jacobi, Given’s and Householder’s methods for symmetric matrices, Rutishauser method for general

matrices, Power and inverse power methods.

UNIT – VII SOLUTION OF DIFFERENTIAL EQUATIONS

Introduction to differential equations, Initial value problems, Euler’s methods, Heun’s method, RungeKutta

methods, Taylor series method, Predictor-Corrector methods, Systems of differential equations,

Boundary valve problems, Finite-difference method, Solution of problems through a structured

programming language such as C or Pascal.

UNIT – VIII PARTIAL DIFFERENTIAL EQUATIONS, EIGENVALUES AND EIGENVECTORS

Solution of hyperbolic, parabolic and elliptic equations, The eigenvalue problem, The power method and

the Jacobi’s method for eigen value problems, Solution of problems through a structural programming

language such as C or Pascal.