Asymptotic analysis | Approximations

WKB approximation

In mathematical physics, the WKB approximation or WKB method is a method for finding approximate solutions to linear differential equations with spatially varying coefficients. It is typically used for a semiclassical calculation in quantum mechanics in which the wavefunction is recast as an exponential function, semiclassically expanded, and then either the amplitude or the phase is taken to be changing slowly. The name is an initialism for Wentzel–Kramers–Brillouin. It is also known as the LG or Liouville–Green method. Other often-used letter combinations include JWKB and WKBJ, where the "J" stands for Jeffreys. (Wikipedia).

WKB approximation
Video thumbnail

Approximating Functions in a Metric Space

Approximations are common in many areas of mathematics from Taylor series to machine learning. In this video, we will define what is meant by a best approximation and prove that a best approximation exists in a metric space. Chapters 0:00 - Examples of Approximation 0:46 - Best Aproximati

From playlist Approximation Theory

Video thumbnail

The Logarithm -- limit definition #shorts

Here's a quick derivation of the limit definition for the logarithm. A previous video, https://youtu.be/bPmooEEXU_8 , relied on this definition. You can read about this derivation here: https://medium.com/mathadam/fall-in-love-with-e-all-over-again-2ddc5d03d4cc?sk=8f7111156005f8db169a628a9

From playlist e

Video thumbnail

Linear Algebra 6.4 Best Approximation; Least Squares

My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.

From playlist Linear Algebra

Video thumbnail

Linear Algebra 6.6 Function Approximation; Fourier Series

My notes are available at http://asherbroberts.com/ (so you can write along with me). Elementary Linear Algebra: Applications Version 12th Edition by Howard Anton, Chris Rorres, and Anton Kaul A. Roberts is supported in part by the grants NSF CAREER 1653602 and NSF DMS 2153803.

From playlist Linear Algebra

Video thumbnail

Find the Linearization of f(x, y) = sqrt(20 - x^2 - 7y^2) at (2, 1) and Approximate f(1.95, 1.08)

Find the Linearization of f(x, y) = sqrt(20 - x^2 - 7y^2) at (2, 1) and Approximate f(1.95, 1.08). This is a calculus 3 problem. If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com Free Homework Help : https

From playlist Tangent Planes and Linear Approximation

Video thumbnail

Find the Tangent Line Approximation L(x, y) of f(x, y) = tan^(-1)(x + 2y) at (1, 0)

Find the Tangent Line Approximation L(x, y) of f(x, y) = tan^(-1)(x + 2y) at (1, 0). This is also called the linearization. This is a calculus 3 problem. If you enjoyed this video please consider liking, sharing, and subscribing. Udemy Courses Via My Website: https://mathsorcerer.com F

From playlist Tangent Planes and Linear Approximation

Video thumbnail

Linear Approximations and Differentials

Linear Approximation In this video, I explain the concept of a linear approximation, which is just a way of approximating a function of several variables by its tangent planes, and I illustrate this by approximating complicated numbers f without using a calculator. Enjoy! Subscribe to my

From playlist Partial Derivatives

Video thumbnail

Polynomial approximations -- Calculus II

This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.

From playlist Calculus II

Video thumbnail

L8.3 Deriving the connection formulae

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L8.3 Deriving the connection formulae License: Creative Commons BY-NC-SA

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Video thumbnail

L7.2 Approximate WKB solutions

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L7.2 Approximate WKB solutions License: Creative Commons BY-NC-SA More in

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Video thumbnail

L7.1 The WKB approximation scheme

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L7.1 The WKB approximation scheme License: Creative Commons BY-NC-SA More

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Video thumbnail

L7.3 Validity of the WKB approximation

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L7.3 Validity of the WKB approximation License: Creative Commons BY-NC-SA

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Video thumbnail

Taylor polynomials -- Calculus II

This lecture is on Calculus II. It follows Part II of the book Calculus Illustrated by Peter Saveliev. The text of the book can be found at http://calculus123.com.

From playlist Calculus II

Video thumbnail

Black hole perturbation theory (Lecture 3) by Emanuele Berti

DATES Monday 25 Jul, 2016 - Friday 05 Aug, 2016 VENUE Madhava Lecture Hall, ICTS Bangalore APPLY Over the last three years ICTS has been organizing successful summer/winter schools on various topics of gravitational-wave (GW) physics and astronomy. Each school from this series aimed at foc

From playlist Summer School on Gravitational-Wave Astronomy

Video thumbnail

L6.5 Semiclassical approximation and local de Broglie wavelength

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L6.5 Semiclassical approximation and local de Broglie wavelength License:

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Video thumbnail

L15.1 Classical analog: oscillator with slowly varying frequency

MIT 8.06 Quantum Physics III, Spring 2018 Instructor: Barton Zwiebach View the complete course: https://ocw.mit.edu/8-06S18 YouTube Playlist: https://www.youtube.com/playlist?list=PLUl4u3cNGP60Zcz8LnCDFI8RPqRhJbb4L L15.1 Classical analog: oscillator with slowly varying frequency License:

From playlist MIT 8.06 Quantum Physics III, Spring 2018

Video thumbnail

Lec 20 | MIT 5.80 Small-Molecule Spectroscopy and Dynamics, Fall 2008

Lecture 20: Transformations between basis sets: 3-j, 6-j, and Wigner-Eckart theorem Instructor: Robert Field License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 5.80 Small-Molecule Spectroscopy and Dynamics, Fall 2008

Related pages

Slowly varying envelope approximation | Ansatz | Schrödinger equation | Divergent series | Harold Jeffreys | Eikonal equation | Supersymmetric WKB approximation | George Green (mathematician) | Method of matched asymptotic expansions | Action (physics) | Method of dominant balance | Method of steepest descent | Steven Orszag | Instanton | Airy function | Joseph Liouville | Stationary point | Lagrangian Grassmannian