Maksud "Maclaurin's series" dalam kamus Corsica

ETIMOLOGI PERKATAAN MACLAURIN'S SERIES

Named after Colin Maclaurin (1698–1746), British mathematician who formulated it.

Etimologi adalah kajian asal perkataan dan perubahan struktur dan makna mereka.

SEBUTAN MACLAURIN'S SERIES DALAM CORSICA

Maclaurin's series  [məˈklɔːrɪnz]

APAKAH MAKSUD MACLAURIN'S SERIES dalam CORSICA?

Siri Taylor

Taylor series

Dalam matematik, siri Taylor adalah perwakilan fungsi sebagai jumlah tak terhingga terma yang dikira dari nilai derivatif fungsi pada satu titik. Konsep siri Taylor ditemui oleh ahli matematik Scotland James Gregory dan secara rasmi diperkenalkan oleh ahli matematik Inggeris Brook Taylor pada tahun 1715. Jika siri Taylor berpusat pada sifar, maka siri itu juga dipanggil siri Maclaurin, yang dinamai ahli matematik Scotland Colin Maclaurin, yang menggunakan banyak kes siri Taylor dalam abad ke-18 ini. Ia adalah amalan biasa untuk menghampiri fungsi dengan menggunakan sebilangan segi terma siri Taylor. Teorema Taylor memberikan anggaran kuantitatif mengenai ralat dalam penghampiran ini. Sebilangan nombor terma awal siri Taylor fungsi disebut polynomial Taylor. Serangkaian fungsi Taylor adalah had polynomial Taylor yang berfungsi, dengan syarat had itu ada. Fungsi mungkin tidak sama dengan siri Taylornya, walaupun siri Taylornya menumpu pada setiap titik.

In mathematics, a Taylor series is a representation of a function as an infinite sum of terms that are calculated from the values of the function's derivatives at a single point. The concept of a Taylor series was discovered by the Scottish mathematician James Gregory and formally introduced by the English mathematician Brook Taylor in 1715. If the Taylor series is centered at zero, then that series is also called a Maclaurin series, named after the Scottish mathematician Colin Maclaurin, who made extensive use of this special case of Taylor series in the 18th century. It is common practice to approximate a function by using a finite number of terms of its Taylor series. Taylor's theorem gives quantitative estimates on the error in this approximation. Any finite number of initial terms of the Taylor series of a function is called a Taylor polynomial. The Taylor series of a function is the limit of that function's Taylor polynomials, provided that the limit exists. A function may not be equal to its Taylor series, even if its Taylor series converges at every point.

Definisi Maclaurin's series dalam kamus Corsica

Takrif siri Maclaurin dalam kamus adalah (matematik) jumlah tak terhingga yang memberi nilai fungsi f (x) dari segi derivatif fungsi yang dinilai pada sifar: f (x) = f (0) + (f ' (0) x) / 1! + (f "(0) x²) / 2! + ... Juga dipanggil: Siri Maclaurin.

TERJEMAHAN MACLAURIN'S SERIES

Cari terjemahan Maclaurin's series kepada 25 bahasa dengan penterjemah Corsica pelbagai bahasa kami.

Terjemahan Maclaurin's series dari Corsica ke bahasa lain yang dibentangkan dalam bahagian ini telah diperolehi menerusi terjemahan statistik automatik; di mana unit terjemahan penting adalah perkataan «Maclaurin's series» dalam Corsica.

• Penterjemah Corsica - Cina: 麦克劳林级数
• Penterjemah Corsica - Czech: Serie de Maclaurin
• Corsica: Maclaurin´s series
• Penterjemah Corsica - Hindi: Maclaurin की श्रृंखला
• Penterjemah Corsica - Amhara: سلسلة ماكلورين ل
• Penterjemah Corsica - Rusia: Серия Маклорена
• Penterjemah Corsica - Punjabi: A série de Maclaurin
• Penterjemah Corsica - Basque: ম্যাক্লারিনের সিরিজ
• Penterjemah Corsica - Frisia: La série de Maclaurin
• Penterjemah Corsica - Melayu: Siri Maclaurin
• Penterjemah Corsica - Chichewa: Maclaurin Serie
• Penterjemah Corsica - Jepun: マクローリンのシリーズ
• Penterjemah Corsica - Kreol Haiti: 에 Maclaurin 의 시리즈
• Penterjemah Corsica - Jerman: Seri Maclaurin
• Penterjemah Corsica - Vietnam: Loạt Maclaurin của
• Penterjemah Corsica - Tagalog: மெக்லாரின் தொடர்
• Penterjemah Corsica - Marathi: मॅक्लॉरिनची मालिका
• Penterjemah Corsica - Turki: Maclaurin serisi
• Penterjemah Corsica - Itali: Serie di Maclaurin
• Penterjemah Corsica - Poland: Maclaurin w serii
• Penterjemah Corsica - Ukraine: Серія Маклорена
• Penterjemah Corsica - Romania: Serie Maclaurin lui
• Penterjemah Corsica - Cina: Σειρά Maclaurin του
• Penterjemah Corsica - Afrikaans: Maclaurin se reeks
• Penterjemah Corsica - Swahili: Maclaurin serie
• Penterjemah Corsica - Parsi: Maclaurin serie

CORSICA BUKU YANG BERKAIT DENGAN «MACLAURIN'S SERIES»

Ketahui penggunaan Maclaurin's series dalam pilihan bibliografi berikut. Buku yang berkait dengan Maclaurin's series dan ekstrak ringkas dari yang sama untuk menyediakan konteks penggunaannya dalam kesusasteraan Corsica.

Higher Engineering Mathematics

Develop a series for sinhx using Maclaurin's series. f(x)=sinhx f(0)=sinh0= e0−e− 02=0 f(x)= coshx f(0)= cosh0 = e0+e−02 = 1 f(x)=sinhx f(0)=sinh0=0 f(x)=coshx f(0 )=cosh0= 1 fiv(x)= sinhx fiv(0)= sinh0 = 0 fv(x)=coshx fv(0)=cosh0=1 ...

John Bird,, 2014

Understanding Engineering Mathematics

Now try the following Practice Exercise Practice Exercise 97 Further problems on Maclaurin's series (answers on page 1118) 1. Determine the first four terms of the power series for sin 2x using Maclaurin's series. 2. Use Maclaurin's series to ...

John Bird, 2013

Newnes Engineering Mathematics Pocket Book

x2 X4 and coshx:1+E+E+--. Using a series, called Maclaurin's series, mixed functions containing, say, algebraic, trigonometric and exponential functions, may be expressed solely as algebraic functions, and differentiation and integration can ...

John Bird, 2012

GCE A-level Mathematics Challenging Drill Questions ...

Given that y I (sin'1 x)2, show that 121 (1 Xlidxi —4y 2 and (1—X2)d—l2/—Xfl:2 dx dx By further differentiation, find the Maclaurin's series of y up to and including the term in x4. 3 x Show how the expansion sin'1 x z x +? may be used to verify ...

Thomas Bond, Chris Hughes, 2013

Mathematics for Electrical Technicians 4/5: Level 4-5

The uses of Maclaurin's series include expressing mixed functions, containing some or all of trigonometric, exponential, algebraic and logarithmic terms, in a form where such techniques as Newton's method (see Chapter 2), or approximate ...

J. O. Bird, A. J. C. May, 2014

Textbook of Differential Calculus

This is called Maclaurin's series. Corollary 1 Let y = f(x), y, = f(x), y2 = f'(x), ... Putting x = 0, we write /(0) = (j)o, /'(0) = CvOo, f'(0) = (y2)0, ... Therefore, x2, . x> y = f(x) = (y)o+x(y1)0 +—(y2)0+—(yi)0+--- This is the another form of Maclaurin's series ...

Ahsan Akhtar, Sabiha Ahsan, 2004

Mathematics

Maclaurin's series is a special case of Taylor's series and Taylor's theorem with the Lagranges form of remainder is a simple variation law of the mean. Both the series expansions of a function represent that function for those values and only ...

K.M. Sastry, R.K. Gupta

Engineering Mathematics - I

Thus putting a = 0 and h = x in Taylor's theorem, we get f(x) = f(0)+xf'(0)+^ '"(0) + ^ - HO) + ... + .n-1 (n-1) f(n)(0) + Rn D) Maclaurin's Series If Rn — » 0 as n — > °° then Maclaurin's theorem assumes the form of Maclaurin's series and it is given ...

S.K.Kate, 2009

Engineering Mathematics Pocket Book

Substituting these values into the Maclaurin's series gives: f(x) ln( x) x() x!() x ! ) x! () x ! () 1 0 1 21 3 2 4 6 5 24 2 3 4 5 ( i.e. ln(1x)xx2x3x4x5 ... 2 3 4 5 Application: Find the expansion of (2 x)4 using Maclaurin's series f(x) ( x) f() f(x) ( x) f() () 32 f(x ) ...

John Bird, 2008

GCE A-level Mathematics Challenging Drill Questions ...

2 (1—X2)(%j :4y d_2Y_ Q_ and 1—xZ X ( )dxz dX 2 By further differentiation, find the Maclaurin's series of y up to and including the term in x4. x3 Show how the expansion sin'1 Xz X+€ may be used to verify the answer obtained above. d .

Thomas Bond, Chris Hughes, 2013