Ordinary differential equations

Riccati equation

In mathematics, a Riccati equation in the narrowest sense is any first-order ordinary differential equation that is quadratic in the unknown function. In other words, it is an equation of the form where and . If the equation reduces to a Bernoulli equation, while if the equation becomes a first order linear ordinary differential equation. The equation is named after Jacopo Riccati (1676–1754). More generally, the term Riccati equation is used to refer to matrix equations with an analogous quadratic term, which occur in both continuous-time and discrete-time linear-quadratic-Gaussian control. The steady-state (non-dynamic) version of these is referred to as the algebraic Riccati equation. (Wikipedia).

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Riccati ode

Illustrates the solution of a Riccati 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

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The Definition of a Linear Equation in Two Variables

This video defines a linear equation in to variables and provides examples of the different forms of linear equations. http://mathispower4u.com

From playlist The Coordinate Plane, Plotting Points, and Solutions to Linear Equations in Two Variables

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The golden ratio | Lecture 3 | Fibonacci Numbers and the Golden Ratio

The classical definition of the golden ratio. Two positive numbers are said to be in the golden ratio if the ratio between the larger number and the smaller number is the same as the ratio between their sum and the larger number. Phi=(1+sqrt(5))/2 approx 1.618. Join me on Coursera: http

From playlist Fibonacci Numbers and the Golden Ratio

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Understanding the discriminant as a part of the quadratic formula

👉 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 | x^2+bx+c

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How does the discriminant relate to the quadratic formula

👉 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

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Beltrami Identity Derivation

The Beltrami Identity is a necessary condition for the Euler-Lagrange equation (so if it solves the E-L equation, it solves the Beltrami identity). Here it is derived from the total derivative of the integrand (e.g. Lagrangian).

From playlist Physics

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The discriminant and finding the solutions using quadratic formula

👉 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 | x^2+bx+c

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Classify a polynomial then determining if it is a polynomial or not

👉 Learn how to determine whether a given equation is a polynomial or not. A polynomial function or equation is the sum of one or more terms where each term is either a number, or a number times the independent variable raised to a positive integer exponent. A polynomial equation of functio

From playlist Is it a polynomial or not?

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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

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Martin Larsson: Affine Volterra processes and models for rough volatility

Abstract: Motivated by recent advances in rough volatility modeling, we introduce affine Volterra processes, defined as solutions of certain stochastic convolution equations with affine coefficients. Classical affine diffusions constitute a special case, but affine Volterra processes are n

From playlist Probability and Statistics

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Arthur Krener: "Al'brekht’s Method in Infinite Dimensions"

High Dimensional Hamilton-Jacobi PDEs 2020 Workshop I: High Dimensional Hamilton-Jacobi Methods in Control and Differential Games "Al'brekht’s Method in Infinite Dimensions" Arthur Krener, Naval Postgraduate School Abstract: Al'brekht's method is a way optimally stabilize a finite dimens

From playlist High Dimensional Hamilton-Jacobi PDEs 2020

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Peter Benner: Matrix Equations and Model Reduction, Lecture 5

Peter Benner from the Max Planck Institute presents: Matrix Equations and Model Reduction; Lecture 5

From playlist Gene Golub SIAM Summer School Videos

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Christa Cuchiero: Rough volatility from an affine point of view​

Abstract: We represent Hawkes process and their Volterra long term limits, which have recently been used as rough variance processes, as functionals of infinite dimensional affine Markov processes. The representations lead to several new views on affine Volterra processes considered by Abi

From playlist Probability and Statistics

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Joel Nagloo 11/11/16 Part 1

Title: On the Algebraic Independence Conjecture for the Generic Painlevé Equations

From playlist Fall 2016

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System Identification: Koopman with Control

This lecture provides an overview of the use of modern Koopman spectral theory for nonlinear control. In particular, we develop control in a coordinate system defined by eigenfunctions of the Koopman operator. Data-driven discovery of {K}oopman eigenfunctions for control E. Kaiser, J. N

From playlist Data-Driven Control with Machine Learning

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David Sauzin - On the Resurgent WKB Analysis

Iwill report on a work in progress with F. FAUVET(Université de Strasbourg)and R. SCHIAPPA(University ofLisbon)about the WKB formal expansions solutions to the 1D stationary Schrödinger equation with polynomial coefficients. Our emphasis is on the coequational resurgent structure,

From playlist Resurgence in Mathematics and Physics

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Within-host modelling and stochastic models - II by Daniel Coombs

Dynamics of Complex Systems - 2017 DATES: 10 May 2017 to 08 July 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore This Summer Program on Dynamics of Complex Systems is second in the series. The theme for the program this year is Mathematical Biology. Over the past decades, the focus o

From playlist Dynamics of Complex Systems - 2017

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Roland Malhamé: "Mean Field Games in Energy Systems Applications"

High Dimensional Hamilton-Jacobi PDEs 2020 Workshop III: Mean Field Games and Applications "Mean Field Games in Energy Systems Applications" Roland Malhamé - École Polytechnique de Montréal Abstract: Solar and wind energy power sources, while ubiquitous in many areas around the world, ar

From playlist High Dimensional Hamilton-Jacobi PDEs 2020

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Learn to find the solutions of a quadratic by applying the quadratic formula

👉 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

Related pages

Schwarzian derivative | SciPy | Bernoulli differential equation | Mathematics | Quadratic function | Ordinary differential equation | Univalent function | Matrix difference equation | Algebraic Riccati equation