Math 131 Fall 2018 101018 Continuity and Compactness
Definition: bounded function. Continuous image of compact set is compact. Continuous image in Euclidean space of compact set is bounded. Extreme Value Theorem. Continuous bijection on compact set has continuous inverse. Definition of uniform continuity. Continuous on compact set impl
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Math 131 111416 Sequences of Functions: Pointwise and Uniform Convergence
Definition of pointwise convergence. Examples, nonexamples. Pointwise convergence does not preserve continuity, differentiability, or integrability, or commute with differentiation or integration. Uniform convergence. Cauchy criterion for uniform convergence. Weierstrass M-test to imp
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 131 092816 Continuity; Continuity and Compactness
Review definition of limit. Definition of continuity at a point; remark about isolated points; connection with limits. Composition of continuous functions. Alternate characterization of continuous functions (topological definition). Continuity and compactness: continuous image of a com
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis
Math 131 Spring 2022 041122 Uniform Convergence and Continuity
Exercise: the limit of uniformly convergent continuous functions is continuous. Theorem: generalization. Theorem: pointwise convergence on a compact set + extra conditions guarantees uniform convergence. Digression: supremum norm metric on bounded continuous functions. Definitions.
From playlist Math 131 Spring 2022 Principles of Mathematical Analysis (Rudin)
Math 131 Fall 2018 100818 Limits and Continuity in Metric Spaces
Limits of functions (in the setting of metric spaces). Definition. Rephrasal of definition. Uniqueness of limit. Definition of continuity at a point. Remark on continuity at an isolated point. Relation with limits. Composition of continuous functions is continuous. Alternate (topol
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Pre-Calculus - Boundedness theorem for polynomials
This video covers the boundedness theorem for polynomials. This tells us if the zero we tested while using synthetic division is an upper or lower bound for the zeros. Watch carefully on the criteria that must be satisfied to use this theorem. For more videos please visit http://www.mys
From playlist Pre-Calculus
Convergent sequences are bounded
Convergent Sequences are Bounded In this video, I show that if a sequence is convergent, then it must be bounded, that is some part of it doesn't go to infinity. This is an important result that is used over and over again in analysis. Enjoy! Other examples of limits can be seen in the
From playlist Sequences
Functional Analysis - Part 24 - Uniform Boundedness Principle / Banach–Steinhaus Theorem
Support the channel on Steady: https://steadyhq.com/en/brightsideofmaths Or support me via PayPal: https://paypal.me/brightmaths Watch the whole series: https://bright.jp-g.de/functional-analysis/ Functional analysis series: https://www.youtube.com/playlist?list=PLBh2i93oe2qsGKDOsuVVw-OCA
From playlist Functional analysis
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)
Tuomas Hytonen: Two-weight inequalities meet R-boundedness
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Analysis and its Applications
19/11/2015 - Gustav Holzegel - The Linear Stability of the Schwarzschild Solution
The Linear Stability of the Schwarzschild Solution Under Gravitational Perturbations https://philippelefloch.files.wordpress.com/2015/11/2015-ihp-g-holzegel.pdf
From playlist 2015-T3 - Mathematical general relativity - CEB Trimester
Applications of analysis to fractional differential equations
I show how to apply theorems from analysis to fractional differential equations. The ideas feature the Arzela-Ascoli theorem and Weierstrass' approximation theorem, leading to a new approach for solvability of certain fractional differential equations. When do fractional differential equ
From playlist Mathematical analysis and applications
Uniform Probability Distribution Examples
Overview and definition of a uniform probability distribution. Worked examples of how to find probabilities.
From playlist Probability Distributions
Joseph Silverman, Moduli problems and moduli spaces in algebraic dynamics
VaNTAGe seminar on June 23, 2020. License: CC-BY-NC-SA. Closed captions provided by Max Weinreich
From playlist Arithmetic dynamics
Metric Spaces - Lectures 21, 22 & 23: Oxford Mathematics 2nd Year Student Lecture
For the first time we are making a full Oxford Mathematics Undergraduate lecture course available. Ben Green's 2nd Year Metric Spaces course is the first half of the Metric Spaces and Complex Analysis course. This is the 11th of 11 videos. The course is about the notion of distance. You m
From playlist Oxford Mathematics Student Lectures - Metric Spaces
Adam Jakubowski: Functional convergence for dependent heavy-tailed models
Find this video and other talks given by worldwide mathematicians on CIRM's Audiovisual Mathematics Library: http://library.cirm-math.fr. And discover all its functionalities: - Chapter markers and keywords to watch the parts of your choice in the video - Videos enriched with abstracts, b
From playlist Probability and Statistics
Math 131 Fall 2018 120318 Equicontinuity and Uniform Convergence
Review of previous results. Equicontinuity. Exercise: finite set of uniformly continuous functions is equicontinuous. A uniformly convergent sequence of continuous functions on a compact set is equicontinuous. Theorem of Ascoli-Arzela: a pointwise bounded sequence of equicontinuous fun
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Every Compact Set in n space is Bounded
Every Compact Set in n space is Bounded If you enjoyed this video please consider liking, sharing, and subscribing. You can also help support my channel by becoming a member https://www.youtube.com/channel/UCr7lmzIk63PZnBw3bezl-Mg/join Thank you:)
From playlist Advanced Calculus
Math 131 Fall 2018 111618 Uniform convergence, continued
Review of uniform convergence: definition and Cauchy criterion. Rephrasal of uniform convergence. Weierstrass M-test for uniform convergence of a series. Uniform convergence and continuous functions. Pointwise convergence of a decreasing sequence of continuous functions on a compact se
From playlist Course 7: (Rudin's) Principles of Mathematical Analysis (Fall 2018)
Gustav Holzegel - The Linear Stability of the Schwarzschild Solution...
.. under Gravitational Perturbations Princeton University - January 27, 2016 This talk was part of "Analysis, PDE's, and Geometry: A conference in honor of Sergiu Klainerman."
From playlist Anlaysis, PDE's, and Geometry: A conference in honor of Sergiu Klainerman