What are Taylor series?Date: 04/18/99 at 08:20:05 From: Sandra Springer Subject: Taylor Series What are Taylor Series? What are they needed for? I'm very interested in more information about this topic (books, articles, Internet addresses,...). Thank you for your help. Regards Sandra Springer Date: 04/22/99 at 13:13:30 From: Doctor Nick Subject: Re: Taylor Series Hi Sandra - Taylor series are a kind of power series that can be used to give representations of functions. A power series implicitly defines a functions where it converges; what we often want to do is get a power series that represents a function we have in mind. The use of Taylor series is one way to generate such a power series. The basic idea is that certain functions can be expressed as a series involving their derivatives. One reason Taylor series are important is that they can be used to calculate values of a function efficiently. For instance, note that the exponential function, e^x, is very nearly equal to 1+x+(x^2)/2+(x^3)/6+(x^4)/24 for x near zero (say, x between -1 and 1). This fourth-degree polynomial is the first 5 terms of the Taylor series for e^x. Taylor series are used in calculators and computers to calculate things like e^x, cos x, sin x, and so on, for arbitrary values of x (e.g. e^(0.43), cos(0.311), sin(-3.423)). You can find lots about Taylor series in just about any book on calculus. Most college-level textbooks cover the subject. That's the best way to find out more about them. Try your local library, or ask math teachers in your school if they can help you find a calculus book that covers this subject. Write back if you need more help, or have further questions. Have fun, - Doctor Nick, The Math Forum http://mathforum.org/dr.math/ |
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