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Oxford Calculus Taylors Theorem Explained with Examples and Derivation
>> YOUR LINK HERE: ___ http://youtube.com/watch?v=DULzJmUHN5g
University of Oxford mathematician Dr Tom Crawford derives Taylor's Theorem for approximating any function as a polynomial and explains how the expansion works with two detailed examples. • Test yourself with some exercises on Taylor's Theorem with this FREE worksheet in Maple Learn: https://learn.maplesoft.com/doc/cbv2u... • The video begins by introducing the idea of approximating a function by a polynomial and the condition we choose to implement that allows the coefficients to be derived. By ensuring that both the function and polynomial approximation are equal for all derivatives at a single point, Cauchy's Mean Value Theorem can be applied to give equality. • Taylor's Theorem is demonstrated with two fully worked examples. First, the power series expansion for cos is derived by expanding around zero. Next, a third degree polynomial approximation is calculated for small x, when expanding the function ln(1+sin(x)). • Check your working using the Maple Calculator App – available for free on Google Play and the App Store. • Android: https://play.google.com/store/apps/de... • Apple: https://apps.apple.com/us/app/maple-c... • Other videos in the Oxford Calculus series can be found here: • Oxford Calculus • Finding critical points for functions of several variables: • Oxford Calculus: Finding Critical Poi... • Classifying critical points using the method of the discriminant: • Oxford Calculus: Classifying 2D Criti... • Partial differentiation explained: • Oxford Calculus: Partial Differentiat... • Second order linear differential equations: • Oxford Mathematics Open Day 2021: Dif... • Integrating factors explained: • Oxford Calculus: Integrating Factors ... • Solving simple PDEs: • Oxford Calculus: Solving Simple PDEs • Jacobians explained: • Oxford Calculus: Jacobians Explained • Separation of variables integration technique explained: • Oxford Calculus: Separation of Variab... • Solving homogeneous first order differential equations: • Oxford Calculus: Solving Homogeneous ... • Find out more about the Maple Calculator App and Maple Learn on the Maplesoft YouTube channel: / @maplesoft • Produced by Dr Tom Crawford at the University of Oxford. Tom is an Early-Career Teaching and Outreach Fellow at St Edmund Hall: https://www.seh.ox.ac.uk/people/tom-c... • For more maths content check out Tom's website https://tomrocksmaths.com/ • You can also follow Tom on Facebook, Twitter and Instagram @tomrocksmaths. • / tomrocksmaths • / tomrocksmaths • / tomrocksmaths • Get your Tom Rocks Maths merchandise here: • https://beautifulequations.net/collec...
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