Taylor Series Expansions

A *Taylor series expansion* of a continuous function
is a
*polynomial approximation* of
. This appendix derives
the Taylor series approximation informally, then introduces the
remainder term and a formal statement of Taylor's theorem. Finally, a
basic result on the completeness of polynomial approximation is
stated.

- Informal Derivation of Taylor Series
- Taylor Series with Remainder
- Formal Statement of Taylor's Theorem
- Weierstrass Approximation Theorem
- Points of Infinite Flatness
- Differentiability of Audio Signals

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Center for Computer Research in Music and Acoustics (CCRMA), Stanford University