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 139 Fourier Analysis Lecture 04: Uniqueness of Fourier Series
Uniqueness of Fourier Series: all Fourier coefficients vanish implies function vanishes at points of continuity; absolute convergence of Fourier series implies uniform convergence of Fourier series to the original (continuous) function; twice continuous differentiability implies absolute c
From playlist Course 8: Fourier 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)
Detailed Proof of the Monotone Convergence Theorem | Real Analysis
We prove a detailed version of the monotone convergence theorem. We'll prove that a monotone sequence converges if and only if it is bounded. In particular, if it is increasing and unbounded, then it diverges to positive infinity, if it is increasing and bounded, then it converges to the s
From playlist Real Analysis
Interval of Convergence (silent)
Finding the interval of convergence for power series
From playlist 242 spring 2012 exam 3
Divergence Theorem. In this video, I give an example of the divergence theorem, also known as the Gauss-Green theorem, which helps us simplify surface integrals tremendously. It's, in my opinion, the most important theorem in multivariable calculus. It is also extremely useful in physics,
From playlist Vector Calculus
The Difference Between Pointwise Convergence and Uniform Convergence
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys The Difference Between Pointwise Convergence and Uniform Convergence
From playlist Advanced Calculus
Hans G. Feichtinger: Mathematical and numerical aspects of frame theory - Part 2
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
Math 031 041217 Radius of Convergence of a Power Series
Review of the form of a domain of convergence for a power series. Crucial lemma: convergence at a point implies absolute convergence on an interval. Examples of finding the radius of convergence (using root and ratio tests). Facts about power series: sums, products, derivatives, and ant
From playlist Course 3: Calculus II (Spring 2017)
Unlinked fixed points of Hamiltonian...spectral invariants - Sobhan Seyfaddini
Sobhan Seyfaddini Massachusetts Institute of Technology April 17, 2015 Hamiltonian spectral invariants have had many interesting and important applications in symplectic geometry. Inspired by Le Calvez's theory of transverse foliations for dynamical systems of surfaces, we introduce a new
From playlist Mathematics
Asymptotic properties of Kalman filter by Amit Apte
Indian Statistical Physics Community Meeting 2016 URL: https://www.icts.res.in/discussion_meeting/details/31/ DATES Friday 12 Feb, 2016 - Sunday 14 Feb, 2016 VENUE Ramanujan Lecture Hall, ICTS Bangalore This is an annual discussion meeting of the Indian statistical physics community wh
From playlist Indian Statistical Physics Community Meeting 2016
Pseudo-Holomorphic Curves and Approximations of Zero Entropy Hamiltonian Systems... - Barney Bramham
Pseudo-Holomorphic Curves and Approximations of Zero Entropy Hamiltonian Systems by Periodic Ones Barney Bramham Institute for Advanced Study September 20, 2011
From playlist Mathematics
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)
Mohammad Farazmand: "Accelerated Gradient Optimization: A Multiscale Analysis"
Machine Learning for Physics and the Physics of Learning 2019 Workshop III: Validation and Guarantees in Learning Physical Models: from Patterns to Governing Equations to Laws of Nature "Accelerated Gradient Optimization: A Multiscale Analysis" Mohammad Farazmand - North Carolina State Un
From playlist Machine Learning for Physics and the Physics of Learning 2019
Dynamics and Critical Scaling - Gérard Ben Arous
Probability Seminar Topic: High-Dimensional Limit Theorems for Stochastic Gradient Descent: Effective Dynamics and Critical Scaling Speaker: Gérard Ben Arous Affiliation: Courant Institute Date: February 24, 2023 This is a joint work with Reza Gheissari (Northwestern) and Aukosh Jaganna
From playlist Mathematics
Stanford Seminar - Safety-Critical Control of Dynamic Robots
Aaron Ames Caltech February 14, 2020 Science fiction has long promised a world of robotic possibilities: from humanoid robots in the home, to wearable robotic devices that restore and augment human capabilities, to swarms of autonomous robotic systems forming the backbone of the cities of
From playlist Stanford AA289 - Robotics and Autonomous Systems Seminar
CERIAS Security: Automatic Debugging and Verification of RTL-Specified Real-Time Systems 4/6
Clip 4/6 Full title: Automatic Debugging and Verification of RTL-Specified Real-Time Systems via Incremental Satisfiability Counting and On-Time and Scalable Intrusion Detection in Embedded Systems Speaker: Dr. Albert M. K. Cheng · University of Houston Real-time logic (RTL) is use
From playlist The CERIAS Security Seminars 2007
Invariant Measures for Non-autonomous systems.... by Sergey Kryzhevich
PROGRAM SMOOTH AND HOMOGENEOUS DYNAMICS ORGANIZERS: Anish Ghosh, Stefano Luzzatto and Marcelo Viana DATE: 23 September 2019 to 04 October 2019 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Ergodic theory has its origins in the the work of L. Boltzmann on the kinetic theory of gases.
From playlist Smooth And Homogeneous Dynamics
Rate-Induced Tipping in Asymptotically Autonomous Dynamical Systems: Theory.. by Sebastian Wieczorek
PROGRAM TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID) ORGANIZERS: Partha Sharathi Dutta (IIT Ropar, India), Vishwesha Guttal (IISc, India), Mohit Kumar Jolly (IISc, India) and Sudipta Kumar Sinha (IIT Ropar, India) DATE: 19 September 2022 to 30 September 2022 VENUE: Ramanujan Lecture Hall an
From playlist TIPPING POINTS IN COMPLEX SYSTEMS (HYBRID, 2022)
Here I evaluate an integral with a limit, using the celebrated Dominated Convergence Theorem. Come and watch this video, this is pure mathematics at its finest! Link to the math blog: https://www.math3ma.com/blog/dominated-convergence-theorem Dominated Convergence Theorem: https://youtu.b
From playlist Real Analysis