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...July chapter numerical dierentiation uri m ascher and chen greif department of computer science the university british columbia cs ubc ca slides for book afirst course in methods published by siam http www ec securehost com html goals this to develop useful formulas approximating derivatives a function f x at point understand mild stability limitations see techniques action some more advanced applications outline deriving using taylor series richardson extrapolation polynomial interpolation roundo data errors matrices motivation what is given that dierentiable vicinity it often necessary estimate derivative higher nearby values example provides simple instance here we consider complete picture ask how achieve order dierence an easy orderly fashion control or altogether avoid strong cancellation error eect demonstrated these several other questions are considered...