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.

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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