Introduction to the Weierstrauss Approximation Theorem // A Proof with Bernstein Polynomials скачать в хорошем качестве

Introduction to the Weierstrauss Approximation Theorem // A Proof with Bernstein Polynomials

I show how to prove the Weierstrauss approximation theorem in this lecture, which states that every continuous function may be approximated by polynomials to any accuracy. We follow a method introduced by Bernstein that gives a constructive proof. This is a complete lecture that gives an introduction to the Weierstrauss theorem. Bernstein's constructive proof is much more accessible than Weiestrauss' original proof and here I presented it to my undergraduate Numerical Analysis students. WATCH NEXT: Taylor Series:    • Lecture 4 - Taylor Series   Polynomial Interpolation: How Now to Blow Up a Spaceship -    • How to not blow up a spaceship - Polynomia...   Splines and Computer Graphics -    • Splines and Computer Graphics   Music: Flames by Dan Henig Flowers in Heaven by Craig Hardgrove Chomber by Craig Hardgrove Guardians + Tek by Craig Hardgrove 0:00 Start 3:04 White Board Start - Weierstrauss Approximation Theorem 10:29 Bernstein Polynomials 14:05 Properties of Bernstein Polynomials 21:20 Weiestrauss Theorem Proof 41:38 A Bernstein Identity 46:59 Closing Remarks