 |
|
| |
|
|
|
at Global Oneness Community.
Share your dreams and let others help you with the interpretation!
Dream Sharing Forum
|
|
Ordinary differential equation - General application | | Ordinary differential equation - General application: Encyclopedia II - Ordinary differential equation - General application | | An important special case is when the equations do not involve x. These differential equations may be represented as vector fields. This type of differential equation has the property that space can be divided into equivalence classes based on whether two points lie on the same solution curve. Since the laws of physics are believed not to change with time, the physical world is governed by such different ...
See also:Ordinary differential equation, Ordinary differential equation - Definition, Ordinary differential equation - General application, Ordinary differential equation - Existence and nature of solutions, Ordinary differential equation - Types of differential equations with some history, Ordinary differential equation - Homogeneous linear ODEs with constant coefficients, Ordinary differential equation - Linear ODEs with constant coefficients, Ordinary differential equation - Linear ODEs with variable coefficient, Ordinary differential equation - General solution method for first-order linear ODEs, Ordinary differential equation - Linear PDEs, Ordinary differential equation - First-order PDEs, Ordinary differential equation - Singular solutions, Ordinary differential equation - Reduction to quadratures, Ordinary differential equation - The Fuchsian theory, Ordinary differential equation - Lie's theory, Ordinary differential equation - Bibliography | | | Ordinary differential equation, Ordinary differential equation - Bibliography, Ordinary differential equation - Definition, Ordinary differential equation - Existence and nature of solutions, Ordinary differential equation - First-order PDEs, Ordinary differential equation - General application, Ordinary differential equation - General solution method for first-order linear ODEs, Ordinary differential equation - Homogeneous linear ODEs with constant coefficients, Ordinary differential equation - Lie's theory, Ordinary differential equation - Linear ODEs with constant coefficients, Ordinary differential equation - Linear ODEs with variable coefficient, Ordinary differential equation - Linear PDEs, Ordinary differential equation - Reduction to quadratures, Ordinary differential equation - Singular solutions, Ordinary differential equation - The Fuchsian theory, Ordinary differential equation - Types of differential equations with some history, Examples of differential equations, Differential equations of mathematical physics, Differential equations from outside physics, Difference equation, Laplace transform applied to differential equations, Boundary value problem, List of dynamical systems and differential equations topics | | |
| | | Ordinary differential equation: Encyclopedia II - Ordinary differential equation - General application
Ordinary differential equation - General application
An important special case is when the equations do not involve x. These differential equations may be represented as vector fields. This type of differential equation has the property that space can be divided into equivalence classes based on whether two points lie on the same solution curve. Since the laws of physics are believed not to change with time, the physical world is governed by such differential equations. (See also symplectic topology for abstract discussion.)
In the case where the equations are linear, the original equation can be solved by breaking it down into smaller equations, solving those, and then adding the results back together. Unfortunately, many of the interesting differential equations are non-linear, which means that they cannot be broken down in this way. There are also a number of techniques for solving differential equations using a computer (see numerical ordinary differential equations).
Ordinary differential equations are to be distinguished from partial differential equations where y is a function of several variables, and the differential equation involves partial derivatives.
Other related archivesAbelian integrals, Bernoullis, Boole, Boundary value problem, Cauchy, Cauchy-Kovalevskaya theorem, Clairaut, Clebsch, Cramer's rule, Darboux, Difference equation, Differential equations from outside physics, Differential equations of mathematical physics, Euler, Euler's formula, Examples of differential equations, Gauss, Im(y), Jacobi, Jean Bernoulli, Lagrange, Laplace transform applied to differential equations, Leibniz, Levy, Lie, Lie groups, Lie's, Lipschitz condition, List of dynamical systems and differential equations topics, Method of undetermined coefficients, Method of variation of parameters, Monge, Newton, Poincaré-Bendixson theorem, Re(y), Riccati, Solving, Wronskian, analysis, analytic function, basis, boundary conditions, complex numbers, conjugate, constants of integration, convergent series, curve, d'Alembert, derivatives, differential calculus, differential equation, differential operator, discriminant, equivalence classes, harmonic oscillator, iff, infinitesimal transformations, integral calculus, linear, linear combination, linear combinations, list of integrals of exponential functions, mathematics, nineteenth century, nondimensionalization, numerical ordinary differential equations, partial derivatives, partial differential equations, quadratic equation, quadratures, singular solution, singular solutions, symplectic topology, total differential equations, variation of parameters, vector fields, zero
 Adapted from the Wikipedia article "General application", under the G.N U Free Docmentation License. Please also see http://en.wikipedia.org/wiki |
|
|
|
More material related to Ordinary Differential Equation can be found here:
|
|
|
« Back
|
Search the Global Oneness web site |
|
|
|
|
|
Sneak-Peek of Global Oneness Community
Hi friend! The Global Oneness Community, the place for information and sharing about Oneness is not really launched yet (you will see there is still some clean up to do) ...but it is now open for a sneak-peek! And if you wish - please register and become one of the very first members to do so! Jonas
Forum Home,
Articles,
Photo Gallery,
Videos,
News,
Sitemap
...and much more!
|
