Recent content by Mathman23

Homework Statement Howdy, Given a matrix \left[\begin{array}{ccc}x_{11} & x_{12}\\x_{21} & x_{12}\end{array}\right] Which has the exponential matrix e^{t\cdot a} When given the eqn x'= Ax + b where b = \left[\begin{array}{c}b_1 \\ b_2\end{array}\right] I know that had it only...

Homework Statement Given D a a closed convex in R4 which consists of points (1,x_2,x_3,x_4) which satisfies that that 0\leq x_2,0 \leq x_3 and that x_2^2 - x_3 \leq 0 The Attempt at a Solution Then to show that either the point a: = (1,-1,0,1) or b:=(1,0,0,-1) is part of the...

undeletable

Homework Statement I need to show that the mean curvature H at p \in S given by H = \frac{1}{\pi} \cdot \int_{0}^{\pi} k_n{\theta} d \theta where k_n{\theta} is the mean curvature at p along a direction makin an angle theta with a fixed direction. Homework Equations I know...

Hi there, You are right :) Then I get $ \int_0^{\pi}Cos[e^{it}]ie^{it}dt and I let u=e^{it} then: du=ie^{it}dt right? so that part is already in the integral so now it's just: $ \int_0^{\pi}Cos[e^{it}]ie^{it}dt=\int_1^{-1}Cos[u]du right? I then get -2Sin[1] I...

Homework Statement Solve I = \int_{\gamma} f(z) dz where \gamma(t) = e^{i \cdot t} and 0 \leq t \leq \pi Homework Equations Do I use integration by substitution?? The Attempt at a Solution If I treat this as a line-integral I get: I = \int_{a}^{b} f(\gamma(t)) \cdot \gamma'(t)...

Hello Hall many thanks for Your answer, By reading your very good explanation I have formulated my solution. Which goes something like this Case (1) let \gamma(t) = r \cdot e^{i \cdot t} then I_{A} = \int_{\gamma} \frac{1}{z-a} dz, where z_A =r \cdot e^{i \cdot t} +a where t...

No I haven't found it in my textbook chapter yet. You mean this? http://en.wikipedia.org/wiki/Residue_theorem

Homework Statement solve the integral \int_{dK(0,1)}\frac{1}{(z-a)(z-b)} dz where |a|,|b| < 1 Homework Equations Would it be relevant to use Cauchys integrals formula here? \int_{C_p} \frac{f(z)-f(z_0)}{z- z_0} dz The Attempt at a Solution If I use the above formula I...

thanks man it did :) Best regards Fred

My post above regardin (2), was just an experiment, but I am unable to argue for f'(z) = f'(0) :( But anyway using post 19 again. how am suppose to get the minus between cos(z_1) * cos(z_2) - sin(z_1) * sin(z_2) = cos(z1 + z_2) Because I multiply by Eulers formula. I get...

Hi again, I have been lookin through (2) again, and I cannot get it to work using euler. I have found in my textbook that exp(z1 + z2) = exp(z1) * exp(z2) Therefore let f(z) = sin(z) \cdot cos(z-c) where z and c belongs to \mathbb{C} Then f'(z) = cos(z) \cdot cos(z-c) -...

Okay thanks, Thought I was too lucky about 1 and 2. by using the euler formula for sin(z1+z2) I get following: \begin{array}{cccc}sin(z_1+z_2) &=& \frac{e^{i \cdot z_1} + e^{- i \cdot z_1}}{2} \cdot \frac{e^{i \cdot z_2} - e^{- i \cdot z_2}}{2i} + \frac{e^{i \cdot z_2} + e^{- i...

Regarding (1) and (2) are they okay too? Any need to try to factor my formula result so they look like the original formulas sin(z1 + z2) = sin(z1) * cos(z2) + sin(z2) * cos(z1) ? or is my way of formulating it consistant?? Best Regards Fred

Hi Just a clean write of part 3, Proof (Part 3): Let z be a complex number. Then according to Eulers formula: sin(z) = \frac{e^{iz} - e^{-iz}}{2i} cos(z) = \frac{e^{iz} + e^{-iz}}{2} Its know that (sin(z))^2 = (\frac{e^{iz} - e^{-iz}}{2i})^2 = -\frac{(e^{iz})^2}{4} +...