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.

---

Subsections

• 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

---

Order a Hardcopy of Mathematics of the DFT

Previous: Appendix: Frequencies Representable by a Geometric Sequence
Next: Informal Derivation of Taylor Series

---

written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.