Theorems in complex analysis | Mathematical principles
In mathematics, the maximum modulus principle in complex analysis states that if f is a holomorphic function, then the modulus |f | cannot exhibit a strict local maximum that is properly within the domain of f. In other words, either f is locally a constant function, or, for any point z0 inside the domain of f there exist other points arbitrarily close to z0 at which |f | takes larger values. (Wikipedia).
Maximum modulus principle In this video, I talk about the maximum modulus principle, which says that the maximum of the modulus of a complex function is attained on the boundary. I also show that the same thing is true for the real and imaginary parts, and finally I discuss the strong max
From playlist Complex Analysis
Complex analysis: Maximum modulus principle
This lecture is part of an online undergraduate course on complex analysis. We prove the maximum modulus principle, and use to to prove the fundamental theorem of algebra and to find the symmetries of the unit disk. For the other lectures in the course see https://www.youtube.com/playli
From playlist Complex analysis
Math 135 Complex Analysis Lecture 12 030315: Maximum Modulus Principle; Harmonic Functions
Mean Value Property of analytic functions; local maximum modulus principle; maximum modulus principle; existence of harmonic conjugate on simply connected sets (and thus locally); Mean Value Property for harmonic functions; maximum modulus principle for harmonic functions; Dirichlet proble
From playlist Course 8: Complex Analysis
Maximum and Minimum of a set In this video, I define the maximum and minimum of a set, and show that they don't always exist. Enjoy! Check out my Real Numbers Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCZggpJZvUXnUzaw7fHCtoh
From playlist Real Numbers
MAXIMUM PRINCIPLE -- Part 1 -- Core Theorems of Complex Analysis
Part 2: https://www.youtube.com/watch?v=jmP4VlgZvb0 Part 3: https://www.youtube.com/watch?v=fLnRDhhzWKQ In this video, we give a proof of the Maximum Principle, which is a monumental result in the subject of complex analysis. The maximum principle is also referred to as the maximum modul
From playlist Complex Analysis
Maximum principle for heat equation In this video, I present the maximum principle, which is a very interesting property of the heat equation: Namely the largest (and smallest) value of solutions is attained either initially, or on the sides! Check out my PDE Playlist: https://www.yout
From playlist Partial Differential Equations
Extreme Value Theorem Using Critical Points
Calculus: The Extreme Value Theorem for a continuous function f(x) on a closed interval [a, b] is given. Relative maximum and minimum values are defined, and a procedure is given for finding maximums and minimums. Examples given are f(x) = x^2 - 4x on the interval [-1, 3], and f(x) =
From playlist Calculus Pt 1: Limits and Derivatives
Free ebook https://bookboon.com/en/partial-differential-equations-ebook What is the maximum principle for partial differential equations and how is it useful? The main result is presented and proved. Such ideas have important applications to understanding the behaviour of solutions to pa
From playlist Partial differential equations
Maximum and Minimum Values (Closed interval method)
A review of techniques for finding local and absolute extremes, including an application of the closed interval method
From playlist 241Fall13Ex3
Gauss' Mean Value Property and the Maximum Modulus -- Complex Analysis 11
⭐Support the channel⭐ Patreon: https://www.patreon.com/michaelpennmath Merch: https://teespring.com/stores/michael-penn-math My amazon shop: https://www.amazon.com/shop/michaelpenn ⭐my other channels⭐ Main Channel: https://www.youtube.com/michaelpennmath non-math podcast: http
From playlist Complex Analysis
QED Prerequisites Scattering 6
In this lesson we review some critical mathematics associated with complex analysis. In particular, the nature of an analytic function, the Cauchy Integral Theorem, and the maximum modulus theorem. After this review we turn back to the dark art of asymptotic analysis and study the very cle
From playlist QED- Prerequisite Topics
Theories of Failure | Strength of Materials
This video lecture will give you a good introduction to theories of failure in Strength of materials.Check https://www.learnengineering.org/theories-of-failure.html to learn more about industrial applications of theories.
From playlist Mechanical Engineering
Seminar In the Analysis and Methods of PDE (SIAM PDE): Alexander Kiselev
Title: The Flow of Polynomial Roots Under Differentiation Date: Thursday, June 2, 2022, 11:30 am EDT Speaker: Alexander Kiselev, Duke University Abstract: The question of how roots of polynomials move under differentiation is classical. Contributions to this subject have been made by Gaus
From playlist Seminar In the Analysis and Methods of PDE (SIAM PDE)
Lecture 1: Roal and Harmonic Analysis by Prof. Thiele
Lecture Series
From playlist Lecture Recordings
Calculus: Absolute Maximum and Minimum Values
In this video, we discuss how to find the absolute maximum and minimum values of a function on a closed interval.
From playlist Calculus
On the Mod p Cohomology for GL_2 (I) by Haoran Wang
Program Recent developments around p-adic modular forms (ONLINE) ORGANIZERS: Debargha Banerjee (IISER Pune, India) and Denis Benois (University of Bordeaux, France) DATE: 30 November 2020 to 04 December 2020 VENUE: Online This is a follow up of the conference organized last year arou
From playlist Recent Developments Around P-adic Modular Forms (Online)