Real analysis | Complex analysis | Series expansions
In mathematics, the Taylor series or Taylor expansion of a function is an infinite sum of terms that are expressed in terms of the function's derivatives at a single point. For most common functions, the function and the sum of its Taylor series are equal near this point. Taylor series are named after Brook Taylor, who introduced them in 1715. A Taylor series is also called a Maclaurin series, when 0 is the point where the derivatives are considered, after Colin Maclaurin, who made extensive use of this special case of Taylor series in the mid-18th century. The partial sum formed by the first n + 1 terms of a Taylor series is a polynomial of degree n that is called the nth Taylor polynomial of the function. Taylor polynomials are approximations of a function, which become generally better as n increases. Taylor's theorem gives quantitative estimates on the error introduced by the use of such approximations. If the Taylor series of a function is convergent, its sum is the limit of the infinite sequence of the Taylor polynomials. A function may differ from the sum of its Taylor series, even if its Taylor series is convergent. A function is analytic at a point x if it is equal to the sum of its Taylor series in some open interval (or open disk in the complex plane) containing x. This implies that the function is analytic at every point of the interval (or disk). (Wikipedia).
In this video we discuss the Taylor Series (and the closely related Maclaurin Series). These are two specific types of Power Series that allow you to approximate a function with derivatives of the function at an expansion point. We show how to derive the Taylor Series coefficients in sin
From playlist Optimization
Free ebook http://tinyurl.com/EngMathYT A lecture that introduces Taylor series (and Maclaurin series) and shows how to calculate them. Plenty of examples are discussed and solved. Such ideas are seen in university mathematics.
From playlist A second course in university calculus.
Taylor and Maclaurin Series - An Introduction
Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Let's start a new chapter! I'm really excited about this series, since Taylor series are dope af! :D Enjoy :) Twitter: https://twitter.com/FlammableMaths Facebook
From playlist Taylor Series
Maclaurin series and applications
Free ebook http://bookboon.com/en/learn-calculus-2-on-your-mobile-device-ebook Basic example on Maclaurin series and some applications. 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 deriv
From playlist A second course in university calculus.
Calculus 2: Infinite Sequences and Series (62 of 86) What is the Taylor Series?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a Taylor series. Next video in the series can be seen at: https://youtu.be/dfX4KwhD8qI
From playlist CALCULUS 2 CH 14 SERIES AND SEQUENCES
Taylor Series and Taylor Polynomials
What is a Taylor series? How to make a Taylor Series for a function. Step by step example of approximating cos(x) around x = 2.
From playlist Calculus
From playlist R. Maclaurin and Taylor Series
Fourier Series Coefficients (where did they come from?)
Learn how to derive the Fourier series coefficients formulas. Remember, a Fourier series is a series representation of a function with sin(nx) and cos(nx) as its building blocks. Meanwhile, a Taylor series is a series representation of a function with x^n as its building blocks. These are
From playlist Fourier Series
Math 031 Spring 2018 042718 Taylor Series associated with a function
Review: operations (differentiation, anti-differentiation, multiplication addition) and power series. Definition of Taylor Series associated with an infinitely differentiable function. Examples of Taylor Series. Example of a Taylor series that does not converge back to the original func
From playlist Course 3: Calculus II (Spring 2018)
How do Taylor series provide intuition for limits? - Week 6 - Lecture 9 - Sequences and Series
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From playlist Ohio State: Calculus Two with Jim Fowler: Sequences and Series | CosmoLearning Mathematics
ME564 Lecture 3: Taylor series and solutions to first and second order linear ODEs
ME564 Lecture 3 Engineering Mathematics at the University of Washington Taylor series and solutions to first and second order linear ODEs Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L03.pdf Matlab code: http://faculty.washington.edu/sbrunton/me564/matlab/L03_TaylorSeries.m C
From playlist Engineering Mathematics (UW ME564 and ME565)
The history of Taylor Series and Maclaurin Series including the works of de Lagny, Halley, Gregory, and Madhava using primary sources whenever possible. Lesson also presents the Taylor Theorem along with visualizations of James Gregory's equations. Finally the video discusses the time peri
From playlist Numerical Methods
Multivariable Taylor Polynomials
Free ebook http://tinyurl.com/EngMathYT A lecture on how to calculate Taylor polynomials and series for functions of two variables. Such ideas are useful in approximation of functions. We show where the polynomial representation comes from.
From playlist Mathematics for Finance & Actuarial Studies 2
The Most Important Math Formula For Understanding Physics
Math is the language of physics, and there's one formula that you'll encounter time and again in your study of physics: the Taylor series. Get the notes for free here: https://courses.physicswithelliot.com/notes-sign-up If I had to name one mathematical theorem that's the most essential f
From playlist Physics Help Room
Complex Analysis L03: Functions of a complex variable, f(z)
This video introduces functions of a complex variable, f(z). Important functions include monomials z^n, the complex exponential exp(z), trigonometric functions sin(z), cos(z), among others. The complex Logarithm will be the subject of the next lecture. @eigensteve on Twitter eigenstev
From playlist Engineering Math: Crash Course in Complex Analysis
What is Taylor's theorem? - Week 6 - Lecture 5 - Sequences and Series
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From playlist Ohio State: Calculus Two with Jim Fowler: Sequences and Series | CosmoLearning Mathematics
Math 031 041717 Getting power series expansions; Introduction to Taylor Series
Recall "properties of power series". Example applications: using the properties to obtain power series. Introduction to Taylor series. Example of Taylor series that does not recover the original function. Example of Taylor series for exponential function; for sine function.
From playlist Course 3: Calculus II (Spring 2017)