Complex variables Definition and 120 Threads

If I have a function f(z) such that limit z --> infinity is finite what do I know about that function? Is it "bounded" or am I still confused about what "bounded" means?

Does \int 1/x dx = ln|x| + c in complex variable theory? Or can we relax the absolute value restraint of ln|x|? (as in, can it be ln(x) + c?)

Homework Statement Let D be a connected domain in R^2 and let u(x,y) be a continuous vector field defined on D. Suppose u has zero circulation and zero flux for any simple closed contour on D. u(x,y) = (u_1(x,y),u_2(x,y)) \Gamma = \int_{c}(u\circ\gamma)tds = 0F=\int_{c}(u\circ\gamma)nds =...

Homework Statement Let D be a connected domain in [tex]R^2[\tex] and let u(x,y) be a continuous vector field defined on D, [tex]u(x,y) = (u_1(x,y),u_2(x,y))[\tex][tex]\Gamma = \int_{c}(u\circ\gamma)tds[\tex] [tex]F=\int_{c}(u\circ\gamma)nds[\tex] Homework Equations The Attempt at a Solution...

I think I just flunked out on the in-class portion of my complex variables midterm. I have a take home exam to work on over the weekend, and it's not going to be easy. I studied for days for this midterm, the prof said it would be on "proofs" so I learned every proof in the book. But, I wish I'd...

I'm studying the proof of the ML inequlity from complex analysis. I don't know what they did in one step of the proof and I was wondering if anyone can explain the step to me. First of all the theorem says: Let f(z) be continuous on a contour C. Then |\int_{c}f(z)dz| \leq ML Where L...

I can't think of how to title the problem I'm having, but this is what the course is called. Complex being imaginary numbers, ie z = a + ic where i is the sqrt of -1. So here is the question that I have no idea where to start with: Construct a sequence {zn} which is bounded and for...

Hi. I am studying on complex variables on my own using Brown and Churchill, 6th edition. so far i am doing pretty good, but i have run into trouble doing a few contour integrals. 1. First off, the authors state that unlike in calculus, where the integral can mean area under the curve, in...

I have to prove that tan^(-1)(z) = i/2 * log[(i+z)/(i-z)] Homework Equations sin^(-1)(z) = -i * log[iz + (1-z^2)^(1/2)] cos^(-1)(z) = -i * log[z + i(1-z^2)^(1/2)] The Attempt at a Solution I've tried a number of attemps. I first tried the most obvious and I did sin^(-1)(z)...

Greetings, I'm working (playing) on a problem involving approximating the arcsin() function. I've attmpted to verify the known derivative of the arcsin function (d(arcsin))/dx = 1/sqrt(1-z^2) I know I have a mistake in my derivation. I've attached an electronic copy of my work...

how to solve two equations involving complex variables?? Hi guys! well! i want to know how can u solve the following two equations simultaenously in order to find out Ix and Iy: (3+j4)Ix - j4Iy=10-------------(1) (2-j4)Ix +j2Iy=0---------------(2) please tell me the best methods to...

I'm wondering if anyone can recommend a good intro to complex variables book for an undergrad (calc1-3,diffeq). Preferably something that can be found cheap on amazon (Dover?)

I am proving that the function f(z) = Arg z is nowhere differentiable by using the definiton of a derivative. I let z = x + yi. Then, if the limit exists, we have f'(z) = lim (/\z -> 0) ( f(z + /\z) - f(z) ) / /\z. (Note that /\ is the triangle symbol) Also, let /\z = p + iq, where p and...

I am majoring in EE and have the option of taking either of these classes. I have to take Calc 1-3, Ordinary DiffE, and Linear Algebra. So after these classes is PDE or Complex Variables more useful to electrical engineers?

Hey all, great site and I look forward to contributing more. For now, a question... For next semester I need to choose between Number Theory or Complex Variables. I am under the impression that complex variables will be the more useful class for my physics education, however I had some concerns...

need some urgent help with basic complex variables (no proofs) Hi: can someone give me examples of the following? (no proofs needed) 1. a non-zero complex number z such that Arg(z^2) "not equal to" 2 Arg z 2. a region in C which is not a domain 3. a non-empty subset of C which has no...

I just signed up to take Applications of Complex Variables next term and wondering if anyone here has the scoop on it. Mainly, what are the main topics and any advice on the class or important parts I should really pay attention to.

How do I solve the following integral using complex variable techniques The integral from 0 to infinity of [x^m/(x^2 + 1)^2]; 1<m<3

So how would one solve the following integral using complex variables?, Integral from 0 to pi of [dx/r +5cos(x)] where 0<r<5

I have several questions on complex variables, so I will just put them all in here. 1. What are the positions and natures of the singularities and the residues at the singularities of the following functions in the z-plane, excluding the point at infinity...