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.