Taylor Expansion of f+df About x?

  • #1

Main Question or Discussion Point

How would one expand f+df about x? I'm messing something up in the process and can't seem to resolve it lol
 

Answers and Replies

  • #2
34,278
10,320
What does f+df mean?
How are they related to x?

There is way too much context missing to answer that.
 
  • #3
It shouldn't matter; f is a function of x (and other variables)...
 
  • #4
pwsnafu
Science Advisor
1,080
85
It shouldn't matter; f is a function of x (and other variables)...
You can't Taylor expand around a variable. You expand around a fixed base point. That's why we write the polynomials terms as ##(x-a)^n##, i.e. expand around a.
 
  • #5
34,278
10,320
It shouldn't matter;
It does matter. Letters without any definition are pointless.
It is like asking "what is x+y?" You cannot answer it (apart from "it is x+y") if you have no idea what x and y are.
 
  • #6
Wow...

I was either communicating poorly or something. I found my answer.

f+df = f +(df/dx)dx + (d2f/dx2)dx2 + ... [The parenthetical terms are partials but not the differentials.]

My favorite is, "It does matter. Letters without any definition are pointless." And to think I wasted all that time learning Algebra! :/
 

Related Threads on Taylor Expansion of f+df About x?

Replies
6
Views
2K
  • Last Post
Replies
3
Views
1K
Replies
3
Views
2K
Replies
2
Views
870
  • Last Post
Replies
14
Views
26K
Replies
1
Views
1K
  • Last Post
Replies
7
Views
4K
  • Last Post
Replies
3
Views
3K
Replies
5
Views
2K
Top