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General idea of Taylor series
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Examples: cosine, sine
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Polynomials
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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
nth 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
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Series expansions are around ONE point (in the previous case: a)
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Not every function has a series expansion around all points in its
domain of definition
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Not every function has a series expansion (at all)
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Even if the function has a formal series expansion, the function might
not be equal to the sum of its series expansion (everywhere / anywhere)
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Some functions have a “radius of convergence”, i.e. the function will
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 Spring '08
 HOROWITZ
 Derivative, Power Series, series expansion

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