I have recently taken Course on Numerical Analysis. It is correspondence course. So i to do self study. I will be glad if someone mentions online videos and elementary books which contains following topics:
Approximate numbers. Significant figures. Ab solute, relative and percentage error. General formula to estimate the error in a function.
Descarte's rule of sings. Location of roots. Bisection, Secant, Regular Falsi, Newton-Raphson Methods, Order of convergence of these methods.
Direct Methods-Gauss Elimination, Gauss-Jordan, LU decomposition, Cholesky Decomposition, Iterative Methods-Jacobi, Gauss-Seidel.
Eigen values-Jacobi Method, Givens' Method, Householder's Method, Power Method, QR Method.
Interpolation - Finite differences, Forward, Backward and central differences, Symbolic Relations, Detection of error using difference table. Divided differences and their properties. Interpolation formulas - Newton's, Gauss', Stirling and Bessel's, Lagrange's.
Numerical differentiation using interpolation formulas.
Numerical integration. General formula. Trapezoidal, Simpson on-third and three-eights formulae. newton-Cote's Formulae.
Euler Method. Euler modified. Picard methods. Runge Kutta second and fourth order methods, Milne-Thompson method.