Recent content by saraaaahhhhhh

Homework Statement Describe how to determine whether an equilibrium is stable or unstable when [d2U/dx2]_0 = 0 From Classical Dynamics - Ch 2 #45 - Marion Thornton 2. Homework Equations AND 3. The Attempt at a Solution When second derivative positive, equilibrium is stable. When...

I am actually looking for a proof as well. You say that is the definition of the Taylor series, but how does one prove that if a function F is analytic, it can be represented by a power series of the form \Sigma^{\infty}_{n=0}a_nz^n where a_n = f^{(n)}(0)/n! My teacher recommended a...

I am pretty sure I'm in the same class as this person...except the no-textbook thing threw me off. (My class has a textbook, albeit one the professor doesn't seem to use.) If we're not in the same class, I am having trouble with the exact same problem, which I didn't think came from a book...I...

I'm not sure what you're saying here. I think you get that they don't exist or are undefined, because there would be 0 on the bottom of a fraction? But I'm not sure where you're going with this.

Just to go ahead and try this: would partial u partial x be y(xy)^(-1/2)? And then partial u partial y be x(xy)^(-1/2)? And both partials of v be 0? This is assuming that sqrt(xy) is just the 'real' part...if f(z) takes the form u + iv. I have a feeling this is wrong, since Cauchy-Riemann is...

I mixed up my original message. I actually got x for the imaginary part and x_0 + 2x + iy for the real part. I still don't see how the x_0 was eliminated in your version of the expansion, above. But the main issue is the fact that I get different values in the second part, evaluating the...

Wouldn't that mean the Cauchy-Riemann equations don't hold? I'm a little unsure on what u would be in this case. Do I need to separate sqrt(|xy|) into the real and imaginary parts? Or can I just assume all is real and then take the partial derivates of u, and the partials of v would just be...

Homework Statement In the title: f(z) = sqrt(|xy|)...show that this satisfies the Cauchy-Riemann equations at z=0, but is not differentiable there. Homework Equations Cauchy-Riemann just states that partial u partial x = partial v partial y and partial u partial y = - partial v partial...

Homework Statement Show that f(z) = zRez is differentiable only at z=0, find f'(0) The Attempt at a Solution This should be easy. I find the limit as z_0 approaches 0 of [f(z+z_0) - f(z)]/(z_0) for this function...expand it out, simplify, and find what the limit is when z_0 is...

This isn't a homework question; I'm sorry if I'm mis-posting, but I thought someone here could help. See this link: http://books.google.com/books?id=1QxenjJL6i0C&printsec=frontcover&dq=intro+complex+analysis&lr=&as_brr=3#PPA56,M1 On page 56, does this book have a misprint in the...

So b would be 1/m, i/n, and 0? And c would be 1+i (all go to infinity), 1, 0, p/m, and iq/n? What about a? Are there no limit points? It doesn't seem to converge anywhere. Except maybe at 1 and 2, when n goes to infinity?

Homework Statement Find the limit points of the set of all points z such that: a.) z=1+(-1)^{n}\frac{n}{n+1} (n=1, 2, ...) b.) z=\frac{1}{m}+\frac{i}{n} (m, n=+/-1, +/-2, ...) c.) z=\frac{p}{m}+i\frac{q}{n} (m, n, p, q=+/1, +/-2 ...) d.) |z|<1 Homework Equations None. The Attempt at a...

I see your point, but I don't know how to generalize the value for the dimension. From what you're saying: in part a.), the basis is simply the set of {1, x, x^2...x^(N-1)} and the vectors are represented by the coefficients {c_0, c_1...c_(N-1)}. Okay, that makes sense. For part b.), the...

Thanks for the tip. I must be confused from what my teacher's notes are saying. He basically said the vectors would be defined as polynomials, like your p(x) above. And this sentence: "Can you suggest a set of simple functions of x that you can combine with constant coefficients that are...

I have never taken linear algebra, but we're doing some catch-up on it in my Quantum Mechanics class. Using the Griffiths book, problem A.2 if you're curious. Please explain how to solve this, if you help me. If you know of resources on how to think about this stuff, I'd greatly appreciate...