Partial differential equations
The Richards equation represents the movement of water in unsaturated soils, and is attributed to Lorenzo A. Richards who published the equation in 1931. It is a quasilinear partial differential equation; its analytical solution is often limited to specific initial and boundary conditions. Proof of the existence and uniqueness of solution was given only in 1983 by Alt and Luckhaus. The equation is based on Darcy-Buckingham law representing flow in porous media under variably saturated conditions, which is stated as where is the volumetric flux; is the volumetric water content; is the liquid pressure head, which is negative for unsaturated porous media; is the unsaturated hydraulic conductivity; is the geodetic head gradient, which is assumed as for three-dimensional problems. Considering the law of mass conservation for an incompressible porous medium and constant liquid density, expressed as , where is the sink term [T], typically root water uptake. Then substituting the fluxes by the Darcy-Buckingham law the following mixed-form Richards equation is obtained: . For modeling of one-dimensional infiltration this divergence form reduces to . Although attributed to L. A. Richards, the equation was originally introduced 9 years earlier by Lewis Fry Richardson in 1922. (Wikipedia).
Illustrates the solution of a Bernoulli first-order differential equation. Free books: http://bookboon.com/en/differential-equations-with-youtube-examples-ebook http://www.math.ust.hk/~machas/differential-equations.pdf
From playlist Differential Equations with YouTube Examples
How to determine the max or min of a quadratic function in vertex form
👉 Learn how to identify the vertex of a parabola by completing the square. A parabola is the shape of the graph of a quadratic equation. A quadratic equation can be written in the standard form (i.e. in the form y = ax^2 + bx + c) or it can be written in the vertex form (i.e. in the form y
From playlist Identify the Vertex of a Quadratic
Introduction to Parametric Equations
This video defines a parametric equations and shows how to graph a parametric equation by hand. http://mathispower4u.yolasite.com/
From playlist Parametric Equations
Factor using the quadratic formula finding real irrational roots
👉 Learn how to solve quadratic equations using the quadratic formula. A quadratic equation is an equation whose highest power on its variable(s) is 2. The quadratic formula is a formula which can be used to find the roots of (solve) a quadratic equation. The quadratic formula is given by
From playlist Solve by Quadratic Formula | ax^2+bx+c
Learn how to write the equation of a parabola given the vertex and a point on the graph
👉 Learn how to write the equation of a parabola given three points. The equation of a parabola is of the form f(x) = ax^2 + bx + c, where a, b and c are constants. Since, the equation of a parabola has 3 constants, three equations and hence three points are needed to solve/obtain the equat
From playlist Write the Equation of a Quadratic Given Vertex and a Point
Differential Equations | Variation of Parameters.
We derive the general form for a solution to a differential equation using variation of parameters. http://www.michael-penn.net
From playlist Differential Equations
Learn how to determine if a point lies on a graph using standard form of a quadratic
👉 Learn how to write the equation of a parabola given three points. The equation of a parabola is of the form f(x) = ax^2 + bx + c, where a, b and c are constants. Since, the equation of a parabola has 3 constants, three equations and hence three points are needed to solve/obtain the equat
From playlist Write the Equation of a Quadratic Given Vertex and a Point
Given a point and vertex find the formula of the parabola
👉 Learn how to write the equation of a parabola given three points. The equation of a parabola is of the form f(x) = ax^2 + bx + c, where a, b and c are constants. Since, the equation of a parabola has 3 constants, three equations and hence three points are needed to solve/obtain the equat
From playlist Write the Equation of a Quadratic Given Vertex and a Point
These are some of the math books that Richard Feynman used to self-study mathematics. Feynman won the Nobel Prize in Physics in 1965. Calculus for the Practical Man: https://amzn.to/3yxcFBl His Physics Books: https://amzn.to/3T9PdDG Trigonometry for the Practical Man: https://amzn.to/3JAQ
From playlist Book Reviews
Michael Harris "Shimura varieties and the search for a Langlands transform" [2012]
Michael Harris, Institut de mathématiques de Jussieu "Shimura varieties and the search for a Langlands transform" The Langlands reciprocity conjectures predict the existence of a correspondence between certain classes of representations of Galois groups of number fields and automorphic re
From playlist Number Theory
Primes and Equations | Richard Taylor
Richard Taylor, Professor, School of Mathematics, Institute for Advanced Study http://www.ias.edu/people/faculty-and-emeriti/taylor One of the oldest subjects in mathematics is the study of Diophantine equations, i.e., the study of whole number (or fractional) solutions to polynomial equ
From playlist Mathematics
The Art of Physics - Robbert Dijkgraaf - 5/11/2018
On May 11 & 12, 2018, Caltech and PMA presented Feynman 100, a celebration of Richard Feynman’s life & legacy on the occasion of his 100th birthday. The May 11 evening event celebrated his broad contributions to science and society as a scientist, teacher, and curious character. Speakers i
From playlist Feynman 100 Evening Celebration - May 11, 2018
2013 Isaac Asimov Memorial Debate: The Existence of Nothing
Watch the 2020 Isaac Asimov Memorial Debate on Alien Life: https://youtu.be/xgESzc3hc2U The concept of nothing is as old as zero itself. How do we grapple with the concept of nothing? From the best laboratory vacuums on Earth to the vacuum of space to what lies beyond, the idea of nothing
From playlist Isaac Asimov Memorial Debate
TEDxCaltech - Stephen Hawking, John Preskill, Rives, Kip Thorne - Finding Things Out
Stephen Hawking is a theoretical physicist and cosmologist, whose scientific books and public appearances have made him an academic celebrity. He is known for his contributions to the fields of cosmology and quantum gravity, especially in the context of black holes. He has also achieved su
From playlist TEDxCaltech - 1/14/11
Richard Gustavson, Manhattan College
April 26, Richard Gustavson, Manhattan College Developing an Algebraic Theory of Integral Equations
From playlist Spring 2022 Online Kolchin seminar in Differential Algebra
Richard Feynman Learned Basic Calculus With This Book
This is the calculus book that Richard Feynman used to learn Calculus. It is part of a series called Mathematics for Self Study. The book is titled Calculus for the Practical Man and it was written by Thompson. Here is a newer edition https://amzn.to/3ZtsipH Great Calculus Book: https://
From playlist Shorts
Learn how to write the equation of a parabola given the vertex and a point
👉 Learn how to write the equation of a parabola given three points. The equation of a parabola is of the form f(x) = ax^2 + bx + c, where a, b and c are constants. Since, the equation of a parabola has 3 constants, three equations and hence three points are needed to solve/obtain the equat
From playlist Write the Equation of a Quadratic Given Vertex and a Point
8ECM Invited Lecture: Richard Nickl
From playlist 8ECM Invited Lectures
Rahul Pandharipande - Enumerative Geometry of Curves, Maps, and Sheaves 3/5
The main topics will be the intersection theory of tautological classes on moduli space of curves, the enumeration of stable maps via Gromov-Witten theory, and the enumeration of sheaves via Donaldson-Thomas theory. I will cover a mix of classical and modern results. My goal will be, by th
From playlist 2021 IHES Summer School - Enumerative Geometry, Physics and Representation Theory
Given a point and vertex learn to write the equation of the parabola
👉 Learn how to write the equation of a parabola given three points. The equation of a parabola is of the form f(x) = ax^2 + bx + c, where a, b and c are constants. Since, the equation of a parabola has 3 constants, three equations and hence three points are needed to solve/obtain the equat
From playlist Write the Equation of a Quadratic Given Vertex and a Point