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Partial differential equations are mathematical equations that involve two or more independent variables, an unknown function, and partial derivatives of the unknown function. Even the explanation is confusing! If, however, anyone chooses to learn about PDE there are classes offered at any institution of higher learning.
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What is the difference between an ordinary differential equation and a partial differential equation?
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
What are the steps on solving equations?
The answer will depend very much on the nature of the equation. The steps required for a one-step equation are very different from the steps required for a partial differential equation. For some equations there are no straightforward analytical methods of solution: only numerical methods.
Who invented differential equations?
Differential equations were invented separately by Isaac Newton and Gottfried Leibniz. This debate on who was the first one to invent it was argued by both Isaac and Gottfried until their death.
What are the applications of ordinary differential equations in mathematics?
Carbon dating would be one thing...
Where can one learn more about algorithmic equations?
There are plenty of places in order for one to learn more about algorithmic equations. However, one might want to check out brief information about algorithmic equations on the website Wikipedia.
What is monge's Method?
Monge's method, also known as the method of characteristics, is a mathematical technique used to solve certain types of partial differential equations. It involves transforming a partial differential equation into a system of ordinary differential equations by introducing characteristic curves. By solving these ordinary differential equations, one can find a solution to the original partial differential equation.
Who developed 4 partial differential equations that are one of the greatest achievements in maths in his ''treatise of electricity and magnetism?
James Clerk Maxwell
What is differential equations as it relates to algebra?
It is an equation in which one of the terms is the instantaneous rate of change in one variable, with respect to another (ordinary differential equation). Higher order differential equations could contain rates of change in the rates of change (for example, acceleration is the rate of change in the rate of change of displacement with respect to time). There are also partial differential equations in which the rates of change are given in terms of two, or more, variables.
What is the difference between an ordinary differential equation and a partial differential equation?
ordinary differential equation is obtained only one independent variable and partial differential equation is obtained more than one variable.
Why x-3 equals 0 is non homogeneous?
Because homogeneous equations normally refer to differential equations. The one in the question is not a differential equation.
What are the steps on solving equations?
The answer will depend very much on the nature of the equation. The steps required for a one-step equation are very different from the steps required for a partial differential equation. For some equations there are no straightforward analytical methods of solution: only numerical methods.
Where can one find information on ordinary differential equations?
A popular website for information on ordinary differential equations is Pauls Online Notes. Great place that teachs you many other equations and other ways to solve problems.
What are the Uses of Cauchy Euler equation?
One thing about math is that sometimes the challenge of solving a difficult problem is more rewarding than even it's application to the "real" world. And the applications lead to other applications and new problems come up with other interesting solutions and on and on... But... The Cauchy-Euler equation comes up a lot when you try to solve differential equations (the Cauchy-Euler equation is an ordinary differential equation, but more complex partial differential equations can be decomposed to ordinary differential equations); differential equations are used extensively by engineers and scientists to describe, predict, and manipulate real-world scenarios and problems. Specifically, the Cauchy-Euler equation comes up when the solution to the problem is of the form of a power - that is the variable raised to a real power. Specific cases involving equilibrium phenomena - like heat energy through a bar or electromagnetics often rely on partial differential equations (Laplace's Equation, or the Helmholtz equation, for example), and there are cases of these which can be separated into the Cauchy-Euler equation.
Who invented differential equations?
Differential equations were invented separately by Isaac Newton and Gottfried Leibniz. This debate on who was the first one to invent it was argued by both Isaac and Gottfried until their death.
Example of total partial and original differential equation?
An ordinary differential equation (ODE) has only derivatives of one variable.
What are the applications of ordinary differential equations in mathematics?
Carbon dating would be one thing...
Why do you need total derivative and partial derivative?
The partial derivative only acts on one the variables on the equations and treats the others as constant.
