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