Recent content by Knissp

Ahlfors book is on "An Introduction to the Theory of Analytic Functions of One Complex Variable". Some references for what I'm looking for are on wikipedia (http://en.wikipedia.org/wiki/Several_complex_variables), but I was wondering if anyone had any experience with such books to recommend...

Can anyone recommend a good textbook for an undergrad who has done real and complex analysis and wants to learn about several complex variables? Thanks!

I completely overlooked that, and it was really bothering me for a long time, but it makes a lot of sense now! Thank you so much office_shredder! :)

Homework Statement What is a real holomorphic function which is not analytic? Homework Equations Theorem from complex analysis: holomorphic functions and analytic functions are the same. Definition 1: A holomorphic function is infinitely differentiable. Definition 2: An analytic function is...

Does anybody know of any good resources for this? Specifically for real analysis, I'm looking for something that covers calculus on manifolds, differential forms, Lebesgue integration, etc. and for functional analysis: metric spaces, Banach spaces, Hilbert spaces, Fourier series, etc. Thanks!

Thanks, that worked perfectly!

Homework Statement Find the Fourier series for y(x)=\begin{cases} A\sin(\frac{2\pi x}{L}) & 0\leq x\leq\frac{L}{2}\\ 0 & \frac{L}{2}\leq x\leq L\end{cases}Homework Equations B_{n}=\frac{2}{L}\int_{0}^{L}y(x)\sin(\frac{n\pi x}{L})dxThe Attempt at a Solution...

Er right that was a typo. Thanks for the help!

Homework Statement A rod of length L and mass m, pivoted at one end, is held by a spring at its midpoint and a spring at its far end, both pulling in opposite directions. The springs have spring constant k, and at equilibrium their pull is perpendicular to the rod. Find the frequency of small...

Homework Statement Justify for which complex values of a does the principal value of z^a have a limit as z tends to 0? Homework Equations z^a = e^{a log(z)} log(z) = log|z| + (i) (arg(z)) The Attempt at a Solution Lim_{z \rightarrow 0} z^a = Lim_{z \rightarrow 0} e^{(a) (log(z))}...

Homework Statement The equation of a conic in polar coordinates is: r = \frac{r_o}{1-\epsilon cos(\theta)}. \epsilon is the eccentricity, 0 for a circle, (0,1) for an ellipse, 1 for a parabola, and >1 for a hyperbola. What is this equation expressed in Cartesian coordinates...

Another way to look at it would be in terms of components. x + 2y = 4 2x + 4y = 8 x=2, y=1 "If I draw out 2*<1,2> + 1*<2,4> it will lead to <4,8>" Look at the x-components of the vectors. It is easy to see how they are the same as the first equation. x+2y = 4 == 1*1 + 2*1 = 4...

EDIT: SORRY, I didn't read the directions. It says, "Answer the following short questions: If true, justify, if false give a counterex- ample." I'm certain that this question is one of the "false" ones, which is why I was so confused. LOL Homework Statement Let f(x, y, z) = y - x. Then the...

Press 2nd, F1 (to get to F6), then "Clear a-z". Apparently, you have the value of .635 stored as x. :-p

In short, yes. Remember that based on the definitions: (1) the dot product of two vectors returns a scalar, and (2) the cross product of two vectors returns a vector. (That's why the dot product is also known as the scalar product and the cross product is also known as the vector product, by...