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jomomma
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http://mathbin.net/906
cant figure this one out
cant figure this one out
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jomomma said:[tex] x\frac{\partial u}{\partial x}+2y\frac{\partial u}{\partial y} + \frac{\partial u}{\partial z} = 3u[/tex]
cant figure this one out
A PDE, or partial differential equation, is an equation that involves partial derivatives of a multivariate function. It is used to describe physical phenomena such as heat flow, fluid dynamics, and electromagnetic fields.
Basic PDEs are essential for understanding many real-world problems in physics, engineering, and other scientific fields. They provide a mathematical framework for modeling and analyzing complex systems and phenomena.
Some common techniques for solving basic PDEs include separation of variables, method of characteristics, and numerical methods such as finite difference and finite element methods.
A simple example of a basic PDE is the heat equation, which describes the distribution of heat in a given region over time. Its solution can be found using the method of separation of variables, resulting in a solution that is a combination of sines and cosines.
There are many resources available for learning more about basic PDEs, including textbooks, online courses, and video lectures. Some popular resources include "Partial Differential Equations for Scientists and Engineers" by Stanley J. Farlow and "A First Course in Partial Differential Equations" by H. F. Weinberger.