lecture_15_taylor_2p - Lecture 15: Taylor series General...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
1 General idea of Taylor series Examples: cosine, sine Polynomials Lecture 15: Taylor series Programming your own series expansions 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 interes 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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
2 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) Some functions have a “radius of convergence”, i.e. the function will
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 5

lecture_15_taylor_2p - Lecture 15: Taylor series General...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online