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...
Urgent Question: Drawing a Convex Hull in Maple
Homework Statement
Drawing a Convex Hull of 5 2D Points...
Homework Equations
None
The Attempt at a Solution
Hi there,
I am trying draw the convex hull of the 5 points x1,x2,x3,x4,x5 below.
Is this the correct way of doing...
Urgent Stereographic projection question...
Homework Statement
Given the unit sphere S^2= \{x^2 + y^2 + (z-1)^2 = 1\}
Where N is the Northpole = (0.0.2) the stereographic projection
\pi: S^2 \sim \{N\} \rightarrow \mathbb{R}^2 carries a point p of the sphere minus the north pole N onto the...
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...
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...
Hi there I got a couple of question regarding the topic above
Homework Statement
(a) Given the integrals
\int \limit_{0}^{i} \frac{dz}{(1-z)^2}
\int_{i}^{2i} (cos(z)) dz
\int_{0}^{i\pi} e^{z} dz
(1)write this as a Line integral on the form \int_{\gamma} f(\gamma(t)) \cdot...
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) -...