mirror of
https://github.com/chubin/cheat.sheets
synced 2024-11-03 15:40:17 +00:00
22 lines
935 B
Plaintext
22 lines
935 B
Plaintext
|
Generate a Taylor series expansion of cos(x) using x, expanding about x = 0 and
|
||
|
|
continuing until a term with x^6. Taylor series about x = 0 are called Maclaurin
|
||
|
|
series.
|
||
|
|
|
||
|
|
Series[Cos[x], {x, 0, 6}]
|
||
|
|
1 - x^2/2 + x^4/24 - x^6/720 + O[x]^7
|
||
|
|
|
||
|
|
The 'O[x]^7' just represents the rest of the series, which we don't care about.
|
||
|
|
If you don't want it displayed, just wrap the call to Series inside a call to
|
||
|
|
Normal: Normal[Series[...]]. This is useful for plotting series.
|
||
|
|
|
||
|
|
Here's the same function, but expanded about a different point, x = 3pi/2:
|
||
|
|
|
||
|
|
Series[Cos[x], {x, 3 Pi/2, 6}]
|
||
|
|
(x-3pi/2) - 1/6*(x-3pi/2)^3 + 1/120*(x-3pi/2)^5 + O[x-3pi/2]^7
|
||
|
|
|
||
|
|
When plotting series, remember to wrap the function in both a call to Normal AND
|
||
|
|
a call to Evaluate: this strips the extra term mentioned previously and tells
|
||
|
|
Mathematica to actually evaluate the function rather than hold it as an expression.
|
||
|
|
|
||
|
|
Plot[Evaluate[Normal[Series[Cos[x], {x, 0, 6}]]], {x, 0, 1}]
|