Edward tylor Taylor formula

Edward tylor's Taylor formula is as follows:

In mathematics, Taylor formula is a formula that uses the information of a function at a certain point to describe the value near it. If the function is smooth enough, Taylor formula can use these derivative values as coefficients to construct a polynomial to approximate the value of the function at this point. Taylor formula also gives the deviation of this polynomial from the actual function value. Here are ten commonly used Taylor expansions:

1、Rn(x) = o((x-a)^n)

2、rn(x)= f(n+ 1)(a+θ(x-a))( 1-θ)^(n+ 1-p)(x-a)^(n+ 1)/(n！ p)

3、rn(x)= f(n+ 1)(a+θ(x-a))(x-a)^(n+ 1)/(n+ 1)！

4、rn(x)= f(n+ 1)(a+θ(x-a))( 1-θ)^n(x-a)^(n+ 1)/n！

5、Rn(x) = [f(n+ 1)(t)(x-t)^n

6、e^(iπ) + 1 = 0

7、f(x)？ =? exp(？ 1/x？ )?

8、y=a^xy'=a^xlna

9、y = arc cosx y'=- 1/√( 1-x^2)

10、y=a^(x+△x)-a^x=a^x(a^△x- 1)

Edward tylor (Edward Taylor,190865438+1October15-September 9, 2003), born in Hungary, was a famous theoretical physicist in the United States. He has taught at the University of California, Berkeley, University of Chicago and other universities, and is known as the "father of hydrogen bombs", but I don't care about this title. Apart from the hydrogen bomb, he has made considerable contributions to many fields of physics.

Taylor immigrated to the United States in A.D. 1930, became one of the early members of the Manhattan Project, and participated in the development of the first atomic bomb. During this period, he was keen to promote the development of the earliest nuclear fusion weapon (hydrogen bomb), but it was not realized until after the end of World War II. After World War II, at a background investigation hearing about Robert Oppenheimer, Taylor gave some controversial testimony to his former colleagues, which made him unpopular in the scientific community. Nevertheless, he continued to seek help from the American government and military research institutions.

In his later years, Taylor published some technical solutions to controversial military and public problems, including a plan to use thermonuclear explosions to excavate ports in Alaska. He is also an enthusiastic supporter of President Reagan's strategic defense plan. 1986 was awarded the silvanus Thayer Award of the United States Military Academy.

Taylor formula proposer

In mathematics, Taylor formula is a formula that uses the information of a function at a certain point to describe the value near it. If the function is smooth enough, Taylor's formula can use these derivative values as coefficients to construct a polynomial to approximate the function value in the neighborhood of the point when the derivative values of the function are known. Taylor formula also gives the deviation of this polynomial from the actual function value.

Taylor formula got its name from British mathematician Brook Taylor. He first described this formula in a letter of 17 12, although he found a special case in james gray Gauri of 167 1. Before 1797, Lagrange first proposed Taylor theorem with remainder.