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lecture_15_taylor_6p

# lecture_15_taylor_6p - Lecture 15 Taylor series Example of...

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1 General idea of Taylor series Examples: cosine, sine Polynomials Programming your own series expansions Lecture 15: Taylor series Taylor series and series expansion General idea of series expansion: a function can be approximated by the sum of its successive derivatives multiplied by the proper polynomials Function of interest n-th derivative of the function (at point a) Series expansion is done around point a Unless the function is a monomial, the sum is infinite Taylor series and series expansion Common misperceptions about Taylor series, and series expansions Series expansions are around ONE point (in the previous case: a) Not every function has a series expansion around all points in its domain of definition Not every function has a series expansion (at all) Even if the function has a formal series expansion, the function might not be equal to the sum of its series expansion (everywhere / anywhere) S f ti h di f ” i th f ti ill Some functions have a “radius of convergence”, i.e. the function will

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lecture_15_taylor_6p - Lecture 15 Taylor series Example of...

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