What is Taylor Series

MYTUTOR SUBJECT ANSWERS

Answers / Maths / A Level / What is Taylor Series

554 views

What is Taylor Series

Technical Definition: A way to approximate (very) smooth functions (for which derivatives up to high orders exist and are continuous)

Simple Definition: Taylor series is the infinite sum of all the terms for a specific function which is a very close approximation to the real value of the function.

Mathematical definition:

f(x) = f(a) + (f^'(a)(x-a))/1! + (f^''(x)(x-a)²)/2! + (f^'''(x)(x-a)³)/3! + ... +

Why do we have an infinite number of terms?:

The more terms we include in our approximated function, the better the approximation to the real value. For a graph this means that it will represent the actual graph function more.

Special Case (Maclaurin Series):

Maclaurin series is based of the Taylor Series, but we choose the function to be around origin (value = 0) rather than anywhere else.

Advantage of using Taylor/Maclaurin series

its allows for incredibly accurate approximations of a function (depending on the number of terms included)

Provide for integration and differentiation of functions to arrive at representations of other function

Disadvantage of using Taylor/Maclaurin series

some calculations become tedious or the series doesn’t converge quickly

many of the functions are limited to a certain domain given a specific range for convergence (some Taylor series are only valid for a small domain)

Andrew C. GCSE Maths tutor, A Level Maths tutor

2 years ago

Answered by Andrew, an A Level Maths tutor with MyTutor

Still stuck? Get one-to-one help from a personally interviewed subject specialist

310 SUBJECT SPECIALISTS

Will W. GCSE Maths tutor, A Level Maths tutor, A Level Further Mathem...

View profile

£36 /hr

Will W.

Degree: Mathematics (Bachelors) - Durham University

Subjects offered:Maths, Physics+ 2 more

“Hi, I'm Will. I study Maths and Physics and really enjoy talking about them. I am patient and caring, so will take the time to refine a student’s understanding.”

5.0

39 reviews | 103 completed tutorials

Save profile

Bukky O. GCSE Maths tutor, 11 Plus Maths tutor, 13 Plus Maths tutor,...

View profile

£20 /hr

Bukky O.

Degree: Maths with Finance (Bachelors) - Exeter University

Subjects offered:Maths, Chemistry

“Hi, I'm Bukky (pronounced book-ee) and my aim is to not only help your child excel in Maths but also hopefully enjoy it too”

1 completed tutorial

Save profile

Praveenaa K. GCSE Further Mathematics tutor, A Level Further Mathema...

View profile

£20 /hr

Praveenaa K.

Degree: Mathematics (Masters) - Bristol University

Subjects offered:Maths, Science+ 4 more

“Top tutor from the renowned Russell university group, ready to help you improve your grades.”

MyTutor guarantee

Save profile

See more A Level Maths tutors

About the author

View profile

Andrew C.

Currently unavailable: for regular students

Degree: Engineering Mathematics (Masters) - Bristol University

Subjects offered:Maths

“My name is Andrew, I'm in my second year studying Engineering Mathematics at Bristol. Ever since I was young I really enjoyed learning Maths, it was challenging yet rewarding. Whether you are struggling or just want to get better....”

MyTutor guarantee

Save profile

Version:	3.45.0
Build:	16acc337b3ec
Time:	2017-06-13T06:44:00Z

MYTUTOR SUBJECT ANSWERS

What is Taylor Series

Still stuck? Get one-to-one help from a personally interviewed subject specialist

310 SUBJECT SPECIALISTS

About the author

You may also like...

Other A Level Maths questions

One-to-one help is at your fingertips