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...
Re: Structural Analysis-"small deformation"
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...
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?
Re: Why am I struggling with Differential Equations??
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...
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.
By the way you can solve for the acceleration of the blocks by solving it as a system vs writing equations for each block. But then you will still have to write and equation for one of the blocks to find the force 'F' that acts between them...
Draw them out as separate and draw Free body diagrams then equations for each block. Your table looks ok for the entire system but you should label 'Fgravity' as 'Fparallel' or something like that indicating that it acts parallel to the ramp. The value of 'Fgravity' is just 'mg' and it acts...
I think you may need to check your moment summation again, but i could be wrong (i just glanced at the problem quick)...
Anyway it seems like you are more stumped on the concept. What you are doing is taking a system (bar in this case) that is being loaded in two ways:
1. applied forces-...
Yes, work is equal to Fx*dx+Fy*dy+Fz*dz where where Fx,Fy,Fz are the force components and dx,dy,dz are the displacement components...but there is another common way to write the the dot product of two vectors that should make quick work of this problem.
I believe what you are looking for is called belt friction. Here is the wiki link that has the basic formula:
http://en.wikipedia.org/wiki/Belt_friction
There are some other sites & videos you could find if you want a full derivation.
I believe this is a very important point that can't be stressed enough. You can read the books and do problems and have a good idea what is going on. But chances are you will have (& should have) questions that arise when learning something new. Even if it seems like a small step and you are...
I think a good way to go about it would be as follows:
1. Try your best to get an idea what rough area of aerospace you want to pursue further work in (though early in your studies it may be just a guess).
2. Figure out what professors work is best inline with your goals.
3. Email the...
Re: Does it take time to "get used" to physics?
I would have to agree with a lot of this. I would also like to add a few things I've personally noticed when studying physics/engineering:
First is that it always seems like I'm a couple years behind on actual understanding. Its not that I...
I agree. This is all I'm trying to say. Everyone will have their opinions and lean one way or another, but trying to be informative while still giving some positive feedback is like walking a tight rope. Its simply a balancing act and I think everyone would benefit (me included) from taking a...
Yes this is true. I like to think of this popular science as kind of a hook. Its easy to get people interested and excited about it. Then as they begin their journey into learning actual basic physics and so on they will hopefully apply that natural curiosity to more realistic problems. Of...