## Search found 9 matches

Tue Apr 13, 2010 11:34 pm UTC
Forum: Mathematics
Topic: What's wrong with this proof? (Complex Analysis)
Replies: 12
Views: 2293

### Re: What's wrong with this proof? (Complex Analysis)

Isn't: \frac{1}{(z-a)^n} its own Laurent series? Can't you just use that the residue of such a function is 0 for n > 1? Or are you not allowed to use Laurent expansions for this proof? When it comes to your method, it is kind of what I usually see in textbooks - relying on the Fundamental Th...
Thu Nov 19, 2009 9:03 am UTC
Forum: Science
Topic: "total mechanical energy of Earth's orbital motion"
Replies: 20
Views: 5321

### Re: "total mechanical energy of Earth's orbital motion"

The virial theorem would relate the average kinetic and average potential energies. In general, you can't just take a point and say that the potential is -2 times the kinetic. From what I can see, calculating the average energies would be much harder than needed. Just calculate each component indivi...
Thu Nov 19, 2009 4:56 am UTC
Forum: Science
Topic: "total mechanical energy of Earth's orbital motion"
Replies: 20
Views: 5321

### Re: "total mechanical energy of Earth's orbital motion"

Mechanical energy always means kinetic and potential. I don't think this is a poorly worded question. I've seen it before a long time ago. You need to find the kinetic energy associated with Earth rotating, then find the kinetic and potential from Earth revolving about the Sun. The potential will be...
Wed Nov 18, 2009 9:32 am UTC
Forum: Mathematics
Topic: Trapeziums in trigonometry
Replies: 3
Views: 917

### Re: Trapeziums in trigonometry

Without seeing a particular example, all I can give you is a general idea of how to proceed. That's because the method would differ slightly depending on factors such as whether or not the bottom angles are both acute, one is acute, or neither is acute. In general, you can view your trapezoid as a r...
Sat Oct 17, 2009 9:22 am UTC
Forum: Mathematics
Topic: So, does this work as a prrof that e^pi*i=-1?
Replies: 39
Views: 4225

### Re: So, does this work as a prrof that e^pi*i=-1?

My favorite way to show Euler's formula is through the differential equation. It's a lot easier to do than compare Taylor Series. f(\theta) = \cos{\theta} + \textbf{i} \sin{\theta} \frac{df}{d\theta} = -\sin{\theta} + \textbf{i} \cos{\theta} \frac{df}{d\theta} = \textbf{i} f(\theta) ...
Sun Oct 04, 2009 4:19 pm UTC
Forum: Science
Topic: Electric field inside a hollow sphere
Replies: 7
Views: 9909

### Re: Electric field inside a hollow sphere

Use Gauss's Law for flux to do this problem. We have two hollow metal spheres that have been charged before being placed into space. Choose your Gaussian surface to be a sphere. Everything falls out quite nicely from symmetry. \oint \! \textbf{E} \, d\textbf{A} = \frac{Q}{\epsilon_0} Then, since eve...
Wed Jun 17, 2009 9:35 am UTC
Forum: School
Topic: What do other countries teach about The united states?
Replies: 78
Views: 9689

### Re: What do other countries teach about The united states?

As with you, the Soviet role is greatly downplayed (political reasons for this, of course, during the cold war, and that perspective is still ingrained). Which is a pity, as I always saw the Battle of Stalingrad as the key turning point. Germany had devoted huge amounts of manpower to operations in...
Mon Jun 15, 2009 8:09 pm UTC
Forum: School
Topic: Grad school in the US with european BSc
Replies: 3
Views: 789

### Re: Grad school in the US with european BSc

I don't know about the trade offs, but I can comment on the application process. Go ahead and follow through on your initial plan to take the GRE and apply in fall. The act of applying opens a file in your name. You can continue to add to that file until a decision is made. That usually means you wi...
Sat Jun 13, 2009 9:53 am UTC
Forum: School
Topic: What do other countries teach about The united states?
Replies: 78
Views: 9689

### Re: What do other countries teach about The united states?

Well, I know mostly what happened, from both perspectives (I took American history), but to sum things up on what Canadians think of 1812: [snip] Wow. I think that is the best word that describes this. One of the primary causes was British impeding French/U.S. trade. Also, the U.S. believed that th...