Hyperbolic partial differential equations
In mathematics, a hyperbolic partial differential equation of order is a partial differential equation (PDE) that, roughly speaking, has a well-posed initial value problem for the first derivatives. More precisely, the Cauchy problem can be locally solved for arbitrary initial data along any non-characteristic hypersurface. Many of the equations of mechanics are hyperbolic, and so the study of hyperbolic equations is of substantial contemporary interest. The model hyperbolic equation is the wave equation. In one spatial dimension, this is The equation has the property that, if u and its first time derivative are arbitrarily specified initial data on the line t = 0 (with sufficient smoothness properties), then there exists a solution for all time t. The solutions of hyperbolic equations are "wave-like". If a disturbance is made in the initial data of a hyperbolic differential equation, then not every point of space feels the disturbance at once. Relative to a fixed time coordinate, disturbances have a finite propagation speed. They travel along the characteristics of the equation. This feature qualitatively distinguishes hyperbolic equations from elliptic partial differential equations and parabolic partial differential equations. A perturbation of the initial (or boundary) data of an elliptic or parabolic equation is felt at once by essentially all points in the domain. Although the definition of hyperbolicity is fundamentally a qualitative one, there are precise criteria that depend on the particular kind of differential equation under consideration. There is a well-developed theory for linear differential operators, due to Lars Gårding, in the context of microlocal analysis. Nonlinear differential equations are hyperbolic if their linearizations are hyperbolic in the sense of Gårding. There is a somewhat different theory for first order systems of equations coming from systems of conservation laws. (Wikipedia).
Hyperbolic trigonometric functions
Definition of the hyperbolic sine and cosine functions from solving second-order differential equation. Join me on Coursera: Matrix Algebra for Engineers: https://www.coursera.org/learn/matrix-algebra-engineers Differential Equations for Engineers: https://www.coursera.org/learn/differe
From playlist Differential Equations
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions. Site: http://mathispower4u.com Blog: http://mathispower4u.wordpress.com
From playlist Differentiation of Hyperbolic Functions
Introduction to Hyperbolic Functions
This video provides a basic overview of hyperbolic function. The lesson defines the hyperbolic functions, shows the graphs of the hyperbolic functions, and gives the properties of hyperbolic functions.
From playlist Using the Properties of Hyperbolic Functions
Hyperbola 3D Animation | Objective conic hyperbola | Digital Learning
Hyperbola 3D Animation In mathematics, a hyperbola is a type of smooth curve lying in a plane, defined by its geometric properties or by equations for which it is the solution set. A hyperbola has two pieces, called connected components or branches, that are mirror images of each other an
From playlist Maths Topics
What are differential equations?
► My Differential Equations course: https://www.kristakingmath.com/differential-equations-course Differential equations are usually classified into two general categories: partial differential equations, which are also called partial derivatives, and ordinary differential equations. Part
From playlist Popular Questions
In this video, I introduce the hyperbolic coordinates, which is a variant of polar coordinates that is particularly useful for dealing with hyperbolas (and 3 dimensional versions like hyperboloids of one sheet or two sheets). Suprisingly (or not), they involve the hyperbolic trig functions
From playlist Double and Triple Integrals
Since we just covered polar equations, let's go over one other way we can graph functions. Parametric equations are actually a set of equations whereby two variables like x and y both depend on the same variable, usually time, and therefore each rectangular coordinate is determined by its
From playlist Mathematics (All Of It)
Calculus 2: Hyperbolic Functions (1 of 57) What is a Hyperbolic Function? Part 1
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what are hyperbolic functions and how it compares to trig functions. Next video in the series can be seen at: https://youtu.be/c8OR8iJ-aUo
From playlist CALCULUS 2 CH 16 HYPERBOLIC FUNCTIONS
Math: Partial Differential Eqn. - Ch.1: Introduction (6 of 42) Partial Derivative Understood
Visit http://ilectureonline.com for more math and science lectures! In this video I will further explain what is partial differential equation by using a graphical example to explain what is a partial derivative of the equation u=f(x,y)=xy^2. Next video in this series can be seen at: ht
From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION
Sascha Husa (2) - Introduction to theory and numerics of partial differential equations
PROGRAM: NUMERICAL RELATIVITY DATES: Monday 10 Jun, 2013 - Friday 05 Jul, 2013 VENUE: ICTS-TIFR, IISc Campus, Bangalore DETAL Numerical relativity deals with solving Einstein's field equations using supercomputers. Numerical relativity is an essential tool for the accurate modeling of a wi
From playlist Numerical Relativity
Math: Partial Differential Eqn. - Ch.1: Introduction (24 of 42) Gen. Form 2nd PDE (2 Partial Deriv.)
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain the 3 possible solutions 1) hyperbolic, 2) parabolic, 3) elliptic to the general form of a 2nd order differential equation limited with only 2 variables. Next video in this series can be seen
From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION
Derivation and Solution of Laplace’s Equation
In this video we show how the heat equation can be simplified to obtain Laplace’s equation. We investigate how to solve Laplace’s equation using separation of variables. Additional videos in this series: -Introduction to Partial Differential Equations (https://youtu.be/THjaxvPBGOU) -Stan
From playlist Partial Differential Equations
Rainer Verch: Linear hyperbolic PDEs with non-commutative time
Motivated by wave or Dirac equations on noncommutative deformations of Minkowski space, linear integro-differential equations of the form (D + sW) f = 0 are studied, where D is a normal or prenormal hyperbolic differential operator on Minkowski spacetime, s is a coupling constant, and W i
From playlist HIM Lectures: Trimester Program "Non-commutative Geometry and its Applications"
How to classify second order PDE
Free ebook https://bookboon.com/en/partial-differential-equations-ebook How to classify second order partial differential equations. We discuss the conditions that lead to a PDE being: hyperbolic; elliptic; or parabolic. Apologies for the frozen head shot. The file got corrupted.
From playlist Partial differential equations
The Maths Problem Matt Parker Couldn't Solve
Train your Complex Number Expertise by trying out Brilliant! =D https://brilliant.org/FlammableMaths Check out my newest video over on @FlammysWood where I craft the new Board! https://youtu.be/UV73SIx8x6s Don't have a Christmas present for your friends yet? Get your hands on my handcrafte
From playlist Differential Equations
A RIDICULOUSLY AWESOME INTEGRAL: The best thing you are going to see this weekend!
Merch :v - https://teespring.com/de/stores/papaflammy Help me create more free content! =) https://www.patreon.com/mathable Leibniz rule: https://www.youtube.com/watch?v=wkh1Y7R1sOw Arctan integral: https://www.youtube.com/watch?v=_zqHrFKJsFY Dirichlet 1: https://www.youtube.com/watch?v=
From playlist Integrals
Weak Hyperbolicity for Singular Flows by Luciana Silva Salgado
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
Computational Methods for Numerical Relativity, Part 1 Frans Pretorius
Computational Methods for Numerical Relativity, Part 1 Frans Pretorius Princeton University July 16, 2009
From playlist PiTP 2009
Free ebook https://bookboon.com/en/partial-differential-equations-ebook How to solve second order PDE with purely second order derivatives. Several examples are discussed, including Laplace's equation.
From playlist Partial differential equations
Math: Partial Differential Eqn. - Ch.1: Introduction (1 of 42) What is a Partial Differential Eqn?
Visit http://ilectureonline.com for more math and science lectures! In this video I will explain what is a partial differential equation. PDE is a differential equation that contains partial derivatives, and the dependent variable in the equation depends on more than 1 independent variab
From playlist PARTIAL DIFFERENTIAL EQNS CH1 INTRODUCTION