Thanks everyone for the input. I think I will likely go with Roman's text; although it is admittedly too long to finish over the short winter break, I hope to get through most of Part I and then touch on chapters 11 and 14 (at least).
Mathwonk - thanks for the reference to your notes, I will...
I am currently a first year graduate student in math, and I am trying to pick a linear algebra book to work through during the winter break. I have already gone through the computational style linear algebra, and I have also gone through Axler's Linear Algebra Done Right. I would like to go...
Awesome - the book doesn't cover path integrals explicitly for two more chapters, good to know they aren't much different than what I already have covered. Thanks!
I have no reason to think that ##\nabla f(x,y,z)=\lambda(x,y,z)## - although I could solve this if I could assume that. The conditions, as far as I can tell, just say that for some scalar field ##h## we have that ##\nabla f(x,y,z) = [h(x,y,z)](x,y,z)##. In particular, I tried this approach: Let...
Homework Statement
If \nabla f(x,y,z) is always parallel to x \hat i + y \hat j + z \hat k, show that f must assume equal values at the points (0,0,a) and (0,0,-a).
The Attempt at a Solution
I tried a number of things - inspecting the values arrived at when computing the cross product of the...
The problem is not asking you to find m(0), the initial mass, but rather the fraction of the initial mass which the rocket would have to burn in order to reach the velocity specified. In your equation, you can treat v_e, m(0), and v(0) as known quantities (you are correct that v(0)=0). You...
It seems to be staring you in the face. You have an equation with essentially one unknown. Where in your equation is your initial mass, and what indicates the fraction of it expended at time t?
Start in pieces. Take the constants to the outside, and you're left with two terms.
\lim_{x\rightarrow 0} \left (\frac{\sin x}{4x}\cdot\frac{5-5\cos 3x}{2} \right) = \frac{5}{8}\lim_{x\rightarrow 0} \left ( \frac{\sin x}{x} - \frac{\sin x \cos 3x}{x} \right)
See if you can take it from there.
Homework Statement
\sum_{n=2}^{\infty} \frac{(-1)^n}{\sqrt{n} + (-1)^n}Homework Equations
This is in the section covering alternating sequences. Leibniz's rule, conditional/absolute convergence, Dirichlet's test, and Abel's tests were all covered.The Attempt at a Solution
I don't know what to...
Homework Statement
I just got done proving Gauss' test, which is given in the book as:
If there is an N\ge 1, an s>1, and an M>0 such that
\frac{a_{n+1}}{a_n}=1 - \frac{A}{n} + \frac{f(n)}{n^s}
where |f(n)|\le M for all n, then \sum a_n converges if A>1 and diverges if A \le 1.
This...
I ended up determining that my solution was correct, and the book's was incorrect through inspection of the graphs of all three functions. Just wanted to post that here in case anyone else had been following.