Infinite products & the Weierstrass factorization theorem
In this video we're going to explain the Weierstrass factorization theorem, giving rise to infinite product representations of functions. Classical examples are that of the Gamma function or the sine function. https://en.wikipedia.org/wiki/Weierstrass_factorization_theorem https://en.wiki
From playlist Programming
Bolzano-Weierstrass Theorem (Direct Proof) In this video, I present a more direct proof of the Bolzano-Weierstrass Theorem, that does not use any facts about monotone subsequences, and instead uses the definition of a supremum. This proof is taken from Real Mathematical Analysis by Pugh,
From playlist Sequences
Multimeter Review / DMM Review / buyers guide / tutorial
A list of my multimeters can be purchased here: http://astore.amazon.com/m0711-20?_encoding=UTF8&node=5 In this video I do a review of several digital multimeters. I compare features and functionality. I explain safety features, number of digits, display count, accuracy and resolution. Th
From playlist Multimeter reviews, buyers guide and comparisons.
Complex analysis: Weierstrass elliptic functions
This lecture is part of an online undergraduate course on complex analysis. We define the Weierstrass P and zeta functions and show they are elliptic. For the other lectures in the course see https://www.youtube.com/playlist?list=PL8yHsr3EFj537_iYA5QrvwhvMlpkJ1yGN
From playlist Complex analysis
Applying reimann sum for the midpoint rule and 3 partitions
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Irreducibility and the Schoenemann-Eisenstein criterion | Famous Math Probs 20b | N J Wildberger
In the context of defining and computing the cyclotomic polynumbers (or polynomials), we consider irreducibility. Gauss's lemma connects irreducibility over the integers to irreducibility over the rational numbers. Then we describe T. Schoenemann's irreducibility criterion, which uses some
From playlist Famous Math Problems
Math 131 Fall 2018 113018 Pointwise Convergent Subsequences of Functions
Clarifying the last part of the construction of Weierstrass's continuous, nowhere-differentiable function. Recall: Bolzano-Weierstrass theorem. Types of boundedness for sequences of functions: pointwise boundedness, uniform boundedness. Showing that a sequence of uniformly bounded conti
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Analysis 1 - Convergent Subsequences: Oxford Mathematics 1st Year Student Lecture
This is the third lecture we're making available from Vicky Neale's Analysis 1 course for First Year Oxford Mathematics Students. Vicky writes: Does every sequence have a convergent subsequence? Definitely no, for example 1, 2, 3, 4, 5, 6, ... has no convergent subsequence. Does every b
From playlist Oxford Mathematics 1st Year Student Lectures
Find the value of the trigonometric expression using inverse
👉 Learn how to evaluate an expression with the composition of a function and a function inverse. Just like every other mathematical operation, when given a composition of a trigonometric function and an inverse trigonometric function, you first evaluate the one inside the parenthesis. We
From playlist Evaluate a Composition of Inverse Trigonometric Functions
Proving Bolzano-Weierstrass with Nested Interval Property | Real Analysis
We prove the Bolzano Weierstrass theorem using the Nested Interval Property. The Bolzano-Weierstrass theorem states every bounded sequence has a convergent subsequence. We will construct a subsequence by bounding our sequence between M and -M, then creating an infinite sequence of nested i
From playlist Real Analysis
Math 131 113016 Heading Towards Ascoli-Arzela
Pointwise bounded sequence of functions on a countable set has a pointwise convergent subsequence (sketch). Remark: uniformly bounded, pointwise convergent sequence on a compact set does not imply existence of a uniformly convergent subsequence. Equicontinuity. Remark: finite collection
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
How to use midpoint rienmann sum with a table
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist The Integral
Foundations of Quantum Mechanics: Completeness
Foundations of Quantum Mechanics: Completeness This lecture is a long and complex proof that every finite vector space is complete. The purpose is to demonstrate some of the methods of real and functional analysis as well as to emphasize the significance of a vector space being finite-dim
From playlist Mathematical Foundations of Quantum Mechanics
Introduction to elliptic curves and BSD Conjecture by Sujatha Ramadorai
12 December 2016 to 22 December 2016 VENUE Madhava Lecture Hall, ICTS Bangalore The Birch and Swinnerton-Dyer conjecture is a striking example of conjectures in number theory, specifically in arithmetic geometry, that has abundant numerical evidence but not a complete general solution. An
From playlist Theoretical and Computational Aspects of the Birch and Swinnerton-Dyer Conjecture
The Weierstrass Definition of the GAMMA FUNCTION! - Proving Equivalence!
Help me create more free content! =) https://www.patreon.com/mathable Merch :v - https://teespring.com/de/stores/papaflammy https://shop.spreadshirt.de/papaflammy 2nd Channel: https://www.youtube.com/channel/UCPctvztDTC3qYa2amc8eTrg Gamma derive: https://youtu.be/0170T
From playlist Limits
Math 131 Fall 2018 112818 Weierstrass's continuous, nowhere differentiable function
Second part of proof of the interaction of uniform convergence and differentiable functions. Weierstrass's construction of a continuous, everywhere non-differentiable function.
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Math 131 120916 Ascoli Arzela and Stone Weierstrass (redone)
Theorem of Ascoli-Arzela.. Stone-Weierstrass Theorem (density of polynomials in the space of continuous functions on a closed interval with respect to the supremum norm metric). (Redid the lecture but perhaps didn't improve it)
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 101 Fall 2017 Bolzano Weierstrass for Sequences
Theorem: any accumulation point of a sequence is a subsequential limit. Theorem: (Bolzano-Weierstrass) Any bounded sequence of real numbers has a convergent subsequence.
From playlist Course 6: Introduction to Analysis (Fall 2017)
How to find the position function given the acceleration function
👉 Learn how to approximate the integral of a function using the Reimann sum approximation. Reimann sum is an approximation of the area under a curve or between two curves by dividing it into multiple simple shapes like rectangles and trapezoids. In using the Reimann sum to approximate the
From playlist Riemann Sum Approximation