Introduction to numerical analysis

Finite digit arithmetic and errors; floating-point arithmetic; propagated error; generated error; error in evaluation of a function f(x) of a single variable x; exercise set1; non-linear equations; bisection method; secant method; regula-falsi method; Newton's method; Muller's method; fixed point method; Newton's method for multiple roots; system of non-linear equations; Newton's methods; fixed point method; exercise set 2; system of linear equations; gauss-elimination method; Gauss-Jordan method; evaluation of determination; Crout's method; inverse of a matrix; condition numbers and errors; III-conditioned system; iterative improvement; iterative methods; Jacobi's method; Gauss Seidel method; relaxation method; exercises set 3; interpolation; Lagrangian interpolating polynomial; error in Lagrangian interpolation; Newton's form of interpolating polynomial; Newton's divided differences; Newton's divided difference from of polynomial; error in Newton's divided difference form; divided differences for repeated abscissas; Newton's forward form and backward form; Newton's forward polynomial; Newton's backward form; hermite interpolating polynomial; price-wise interpolation; upperbound on piecewise linear interpolation; upperbound on piecewise quadratic interpolation; exercises set 4; numerical differential and integration; numerical differentiation and integration; numerical differentiation; numerical integration; numerical integration; Newton-cotes formulas; basic trapezordal rule; composite trapezordal rule; Simpson's 1/3 rule; composite Simpson's 1/3 rule; Simpson's 3/8 rule; composite Simpson's 3/8 rule; method of undermined parameters; Gaussian quadratures; Gaus-legendre quadranture; Gauss-Chebyshev quadrature; Guss-Hermite quadrature; Gauss-Laguerre Quadrature; generating Orthogenal polynomials; exercises set 5; ordinary differential equations; difference equation; differential equations - single step methods; global error in Euler's method and its convergence; runge-kutta methods; multistep methods; Adams-bas Forth formulas; Milne's type formulas; Adams-Moulton formulas; predictor-corrector pairs with modifiers; system of differential equations; exercise set 6.

"An Introduction to Numerical Analysis" is designed for a first course on numerical analysis for students of science and engineering including computer science. The book contains derivation of algorithms for solving engineering and science problems and also deals with error analysis