Taylor Series

  • Thread starter richardlhp
  • Start date
  • #1
13
0

Main Question or Discussion Point

Hi! I am a 16 year old trying to figure out the application of taylor series. I understand most of its uses when applied to functions like e^x, sinx, cosx, but in a mechanics book, i am required to find delta-F, a finite change in a function F. Ostensibly, this appears to be a step that needs the application of taylor series, so can anyone help me to explain slowly and clearly how taylor series can be applied to delta-F? (sorry i do not know how to use symbols and stuff)
 

Answers and Replies

  • #2
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,517
733
[tex]f(x) = f(a) + \frac{f'(a)}{1!}(x-a) + \frac{f''(a)}{2!}(x-a)^2+...[/tex]

If you lop off the higher order terms you have the approximation

[tex]f(x) \doteq f(a) + \frac{f'(a)}{1!}(x-a)[/tex]

or

[tex]f(x) - f(a) \doteq f'(a)(x-a)[/tex]

If x = b you have

[tex]f(b) - f(a) \doteq f'(a)(b-a)[/tex]

In the delta-y notation you might write this as

[tex]\Delta y \doteq f'(x)\Delta x[/tex]

Is that what you are getting at?
 
  • #3
13
0
Yeah! Thanks a lot. Hence for a more accurate value, one can keep the higher order terms?
 
  • #4
LCKurtz
Science Advisor
Homework Helper
Insights Author
Gold Member
9,517
733
Yeah! Thanks a lot. Hence for a more accurate value, one can keep the higher order terms?
Yes, exactly, as long x is within the radius of convergence from a. Many functions have good approximation with just a few terms for x near a but not every function's Taylor series converges to it.
 
  • #5
2
0

Related Threads for: Taylor Series

  • Last Post
Replies
8
Views
3K
  • Last Post
Replies
2
Views
1K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
5
Views
644
  • Last Post
Replies
2
Views
4K
  • Last Post
Replies
7
Views
2K
  • Last Post
Replies
12
Views
4K
  • Last Post
Replies
7
Views
699
Top