How to understand Taylor/Mclaurin series?

  • Context: Undergrad 
  • Thread starter Thread starter Jrohazn
  • Start date Start date
  • Tags Tags
    Series
Click For Summary

Discussion Overview

The discussion revolves around understanding Taylor and Maclaurin series, particularly in the context of a Calculus 2 course. Participants share their confusion regarding the concepts and seek clarification on how to approach these series, including their definitions and applications.

Discussion Character

  • Homework-related
  • Conceptual clarification
  • Technical explanation

Main Points Raised

  • One participant expresses difficulty in understanding Taylor series, despite being able to work with Maclaurin series and derivatives.
  • Another participant notes that Maclaurin series are a special case of Taylor series, specifically when expanded around the point x=0.
  • Several participants recommend various online resources, including Paul's online notes and Khan Academy videos, as helpful references for understanding Taylor series.
  • One participant describes the Taylor series as a way to express a function as an infinite summation of terms involving constants and increasing powers of (x-a).
  • A participant mentions the need to find a method to calculate the constants in the Taylor series expansion.

Areas of Agreement / Disagreement

Participants generally agree on the relationship between Maclaurin and Taylor series, but there is no consensus on the best approach to understand Taylor series, as confusion and varying levels of understanding persist.

Contextual Notes

Some participants suggest looking for different explanations or resources, indicating that understanding may depend on the presentation of the material. There is also an acknowledgment of the varying quality of online educational content.

Jrohazn
Messages
2
Reaction score
0
I'm in Calculus 2, and I have a final coming up. I did extremely well in all other sections, but this section is extremely confusing. I can represent functions into a basic MacLaurin series, and I can also take the derivative of a function and find the series through manipulation of the function into 1/1-x and take the integral of that. Taylor series, though, is EXTREMELY confusing. I have no idea what to do, and no matter how hard I try, I can't find the pattern. Please help!
 
Physics news on Phys.org
Jrohazn said:
I'm in Calculus 2, and I have a final coming up. I did extremely well in all other sections, but this section is extremely confusing. I can represent functions into a basic MacLaurin series, and I can also take the derivative of a function and find the series through manipulation of the function into 1/1-x and take the integral of that. Taylor series, though, is EXTREMELY confusing. I have no idea what to do, and no matter how hard I try, I can't find the pattern. Please help!
Maclaurin series are just a special case of Taylor series, expanding the function about the value 0 instead of the more general expansion about a point x=a.
Rather than launch into an explanation of Taylor series from scratch, how about you find a reasonable online explanation and come back here to ask about any parts you don't understand? Paul's online notes are generally very good: http://tutorial.math.lamar.edu/Classes/CalcII/TaylorSeries.aspx

Edit: well, that's an endorsement - we independently picked the same site.
 
  • Like
Likes   Reactions: scottdave
Another endorsement from me for Paul as a reference for all things calculus.
 
Khan Academy has a few well put together videos on Taylor Series.

Here are two




Hope this helps and good luck on your final.
 
this video also is great
 
  • Like
Likes   Reactions: scottdave and FactChecker
MAGNIBORO said:
this video also is great

Knowing the quality of 3Blue1Brown's videos I would certainly recommend that OP check that video out.
 
  • Like
Likes   Reactions: scottdave
Yes that is a good video. I will take a look at some of other 3Blue1Brown videos.
 
Taylor series is just saying "can I rewrite a function as an infinite summation of C(x-a)^(increasing powers)".

So say I have the function 2x. Taylor series asks, can 2x be written as C1(x-a)0 + C2(x-a)1 +C3(x-a)2 +C4(x-a)3 + ...

The answer is yes, and you can do it for any function. To show this, you have to find out a method to calculate the constants C.

Here is a great and simple proof of Taylor Series.
 

Similar threads

  • · Replies 2 ·
Replies
2
Views
2K
Replies
23
Views
4K
  • · Replies 5 ·
Replies
5
Views
17K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 2 ·
Replies
2
Views
2K
  • · Replies 17 ·
Replies
17
Views
4K
  • · Replies 3 ·
Replies
3
Views
3K
  • · Replies 3 ·
Replies
3
Views
2K
  • · Replies 9 ·
Replies
9
Views
2K
  • · Replies 3 ·
Replies
3
Views
2K