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Q: Proof of finite difference method using Taylor series?
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Continue Learning about Calculus

Where is calculus used?

Differential calculus (commonly calculus 1) is used in optimization -- basically finding the best or most likely choice for something. For example, the best movie based on past recommendations, or the best price to sell something at), or the most likely meaning for a word. Series, especially Taylor Series, are used to approximate functions and make computation easier. For example, one can replace e^x with the approximation 1+x+x^2/2, when x is close to 0.


What comes to mind when you hear the word calculus?

The first thing that come up into my mind is numbers, calculation, integrals and derivatives


What are the applicaton of fourier series?

It can be used in function approximation, especially in physics and numerical analysis and system & signals. Actually, the essence is that the basis of series is orthorgonal.


Is the bar exam harder than the series 7?

I've never taken the Bar exam but I have taken the Series 7 Exam and passed my first try with a 94. The Series 7 is very comprehensive and contains information you are not likely to run into as a practicing financial advisor. You best prepare for 8 weeks or more if you have any hope to pass.


Is their a solution for sin cos tan without calculator?

Calculating trigonometric functions, such as sin, cos, tan, requires some fairly involved calculations. If you don't have a calculator, you best use tables. Such functions are calculated with Taylor series; for example, if you want to calculate the sine of an angle, and the angle is specified in degrees, multiply by (pi/180) to convert to radians. Then, having the angle "x" in radians, you can use the formula: sin x = x - x3/3! + x5/5! - x7/7! ... Similarly: cos x = 1 - x2/2! + x4/4! - x6/6! ... Note that, although these are infinite series, they converge pretty quickly, especially for small angles. That means that the individual terms quickly get smaller and smaller.

Related questions

What has the author Daryl L Logan written?

Daryl L. Logan has written: 'A First Course in the Finite Element Method/Book and Disk (The Pws Series in Engineering)' 'A first course in the finite element method' -- subject(s): Finite element method 'A first course in the finite element method' -- subject(s): Finite element method 'A First Course in the Finite Element Method Using Algor' -- subject(s): Algor, Data processing, Finite element method


What is Taylor series method?

f(x)=lnx


What is Taylor series?

give the expansion of Taylor series


What does the acronym FEM stand for?

FEM, known as Finite Element Method, is a method for finding the approximate numerical solutions for a series of equations. The solution is based on elemination and approximating. While there are advantages to using this technique improper use or can cause the output to be meaningless.


How do you find log values?

You look them up in log tables, or use a scientific calculator. The calculators use a method based on the Taylor series.


What is converging in calculus?

In calculus, you say that a series or integral converges if it has a finite value. If it does not converge, the series or integral usually diverges to infinity (that is, it does not have a finite value such as 3, -8, 67 etc.,)


Why is it that if a equals 0 the Taylor's series becomes the maclaurin's series?

Simply because the Maclaurin series is defined to be a Taylor series where a = 0.


What is the difference between a convergent and divergent series?

Those terms are both used to describe different kinds of infinite series. As it turns out, somewhat counter-intuitively, you can add up an infinitely long series of numbers and sometimes get a finite sum. And example of this is the sum of one over n2 where n stands for the counting numbers from 1 to infinity. It converges to a finite sum, and is therefore a convergent series. The sum of one over n is a divergent series, because the sum is infinity.


Derive recursion formula for sin by using Taylor's Series?

the Taylor series of sinx


Is Taylor Swift in a twilight series?

No but Taylor Lautner is. Taylor Lautner is dating Taylor Swift.


Who change the role of Taylor lautner in the eclipse series?

Taylor is still in Eclipse.


How is pi 3.14 found?

The numerical value of pi is often found using a Taylor or Maclaurin series (Taylor series centered at 0).