Recent content by kjohnson

I think the most difficult course mathematically is easily fluid mechanics. It was the first course outside of the math department that relied pretty heavily on differential equations (including partial).

Also another tip...you don't need to worry about splitting the interval up according to the roots, the sign of f(x) will take care of everything. There is nothing wrong with splitting the integral up, but it is not necessary for most simple continuous functions.

That is a good question...from a purely geometric standpoint then yes. But mathematically the area below the x-axis is taken to be negative because the differential area is defined as: dA=f(x)dx and when f(x) is negative then that value of dA will also be negative since dx is positive...

I believe your problem is in the absolute value? The area that is below the x-axis should be counted as negative.

You could try passing some sort of "best fit" function through the data and then simply differentiating that function.

1. Yes you can use finite element method to model the problem. 2. Linear elasticity problems can involve large deformation, as long as the stresses and strains within the material do not exceed the linear region. For example a very thin beam can be bent into a tight radius easily while the...

After doing some thinking I don't know if 'u' can be linear in theta (at least physically). Because if it was linear in theta then at theta=0 'u' would have some value, while at theta=2pi 'u' would have some different value despite the fact that theta=0 and theta=2pi correspond to the same...

Yes, when its linear in theta. How do you know when its linear in theta...thats a good question. I will have to do a little thinking on that one, this stuff is kinda new to me as well ;). Hopefully that gives you at least some idea and if I come up with something I will keep you updated.

Yes if u(r) only then it would surely drop out. But that is not the only way... For a moment ignore the partial and just think of it like a normal derivative, more specifically notice it is a second derivative. When would the second derivative of some function equal zero?

Look at \frac{\partial^2u} {\partial\theta^2} When would this term vanish from the equation...

Differential equations isn't necessarily a "cookbook" class, it just depends on how its studied/who is teaching it. Yes, in many undergrad engineering classes it is taught in a cookbook style, but just because you know a few tools to solve a limited set of problems doesn't mean you understand...

Haha, yeah it is a discussion that could go on forever. I'm not trying to start it, just trying to point out that it is headed that direction.

My thoughts exactly. Look, you can only replace a persons job if it is something repetitive that can be coded and run by a machine (like a factory). Notice you still need people there to monitor the process in case something unexpected happens. Basically this is just society evolving to fit...

This is an interesting conversation that seems to touch on the philosophy of: Is mathematics a tool created used to describe the universe? or Is mathematics the "language" of the universe (i.e. it would exist even without the humans who use it)? This is probably better off for another...

Its just the sum of the friction forces for both blocks. I was not 100% sure how the system approach would work but it seems that if you do it as a system it is the same as if you wrote an equation for each block and added them together canceling out the interaction force 'F' between them.