What does 2nd ord pde tell you? like fxx(x,y)

[brandy]

pure and mixed, what do they tell you about a function?

 

[HallsofIvy]

? Exactly what they say- they tell you about how the function, and its first and second derivatives, are related. If not that I don't know what you are looking for.

 

[brandy]

is there a graphical representation of what it looks like?

 

[cpv]

give values to x and y, and draw it.

 

[blue_raver22]

A 2nd order partial differential equation (PDE) is a mathematical equation that involves partial derivatives of a function with respect to two or more independent variables. In the context of physics and engineering, these equations are used to describe the behavior of physical systems that vary in space and time.

The notation fxx(x,y) in a 2nd order PDE indicates that the equation involves the second partial derivative of a function f with respect to the variable x. This means that the rate of change of the function in the x-direction is being considered. Similarly, the notation fyy(x,y) would indicate the second partial derivative with respect to y, and fxy(x,y) would indicate the mixed partial derivative with respect to both x and y.

Pure 2nd order PDEs only involve second derivatives of a single variable, while mixed 2nd order PDEs involve second derivatives of two or more variables. These equations can tell us a lot about the behavior of a function. For example, they can provide information about the rate of change of a function in different directions, the curvature of the function, and the stability or instability of a system.

In physics, 2nd order PDEs are used to describe a wide range of phenomena, such as heat transfer, fluid dynamics, and electromagnetic fields. In engineering, they are used to model the behavior of structures, materials, and systems.

As a scientist, understanding and solving 2nd order PDEs is crucial for being able to analyze and predict the behavior of complex systems. By studying these equations, we can gain valuable insights into the underlying physical processes and make informed decisions about how to control and manipulate them.