Homework Statement
Prove if f is integrable on [a,b] then \exists c a\leq c \leq b so that \int_a^cf = \int_c^bfThe Attempt at a Solution
I know that you have to use the first fundamental theorem of calculus and start with:
g(x) = \int_a^xf(t)dt-\int_x^bf(t)dt
I'm not sure how to get...
Homework Statement
Prove if f(x) is differentiable at x=a then f'(a)=lim_{h\rightarrow0}\frac{f(a+h)-f(a-h)}{2h}Homework Equations
I know that the derivative is defined as
f'(a)=lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}The Attempt at a Solution
Starting from the definition I used a known...
Homework Statement
I have been asked to prove the following statement:
An accumulation point of a set S is either an interior point or a boundary point of S.
Here is my attempt at a solution:
I started from the definition of accumulation points:
A point is an accumulation point (x_0) when...
Can anyone explain how to relate the bunch length and energy spread of a bunch in an electron storage ring to the longitudinal emittance? Also, if you know of a good reference I could use to look up more information I would really appreciate it. Thanks!
I'm working on a research project involving calculations about various aspects of electron storage rings and have come across the term energy acceptance or energy aperture. Could someone explain to me what is meant by this term? It is used in a lot of literature but I haven't been able to find a...
Hey guys I'm wondering if someone could hep me solve this integral. I've been working at it for a few days now (as part of a project I'm doing over the summer) and have gotten stuck. I think I need to make some substitution but I can't see what it is to make.
-\int\frac{dI}{I(R+BI+CI^2)}
I...