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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.

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  • $\begingroup$ I can recommend “Introduction to Numerical Analysis” from Stoer and Bulirsch. $\endgroup$ – Wauzl Aug 11 '15 at 21:47
  • $\begingroup$ @Wauzl Is it suitable for self study for first course $\endgroup$ – Taylor Ted Aug 11 '15 at 21:49
  • $\begingroup$ You can have a look inside on the amazon page, for example. Tastes are different and I do not know your background. I have to admit, though, that is not exactly easy reading. $\endgroup$ – Wauzl Aug 11 '15 at 21:54

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