Taylor Series

  • Thread starter 1MileCrash
  • Start date
  • #1
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Homework Statement



Find the first 4 nonzero terms of:

[itex]e^{t}cos(t)[/itex]

Homework Equations





The Attempt at a Solution



I am trying to multiply the terms of two known series for my answer, but I'm not sure how to do it efficiently.

Should I list 4 terms of each series, then multiply them as if they were just normal polynomials?

EDIT, I tried doing that and it is completely unfeasible. What's the correct way?
 
Last edited:

Answers and Replies

  • #2
Ray Vickson
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Homework Statement



Find the first 4 nonzero terms of:

[itex]e^{t}cos(t)[/itex]

Homework Equations





The Attempt at a Solution



I am trying to multiply the terms of two known series for my answer, but I'm not sure how to do it efficiently.

Should I list 4 terms of each series, then multiply them as if they were just normal polynomials?

EDIT, I tried doing that and it is completely unfeasible. What's the correct way?
What is "unfeasible" about it? It is unpleasant, maybe, but perfectly feasible. It is not how I would do it, however: I would use derivatives to get the coefficients in the expansion.

RGV
 
  • #3
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I see, so you would take the derivatives evaluated for 0? As the coefficients?

Should I always try that method first?

EDIT: Wait, why would you do it that way? Differentiating that 4 function 4 times would be terrible!
 
  • #4
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Wait, why would you do it that way? Differentiating that 4 function 4 times would be terrible!
It wouldn't be that bad. Give it a try.
 
  • #5
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It wouldn't be that bad. Give it a try.
OK. Will report back.
 
  • #6
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OK, it was definitely a lot easier than I anticipated. Thanks again.

1st:
e^t(cost - sint)

2nd:

-2e^t(sin t)

3rd
-2e^t(cos t + sin t)

4th

-4e^t(cos t)
 

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