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52 views

Applying Green's Theorem to a Closed Complex Contour Integral

How would one apply Green's Theorem to the following complex contour integral: $\oint_\gamma $ $\frac{u^{s-1}}{e^{-u}-1)}du$. Where $\gamma$ is the Hankel Contour (counterclockwise) and R is the ...
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1answer
46 views

Stokes' Theorem and Surfaces

Stokes' Theorem states the following: \begin{equation*} \oint_c \textbf{F}\centerdot d\textbf{r}= \int\int_S (\nabla \times\textbf{F})\centerdot nd \textbf{S}\end{equation*} for a given C that is the ...
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0answers
74 views

Best book for learning multiple integrals, line integrals, greens theorem etc..

I've been searching for a book that teaches multiple integrals and such in a way that I can understand, I need to learn it quickly, so I don't need too much of the intuition, I just need to be able to ...
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1answer
33 views

Integration Exercise.Help!

I have to integrate the function F(x,y)=x+y on the line segment x=t , y=1-t , z=0 from (0,1,0) to (1,0,0) .So what i did is think the line segment as a vector function(curve) σ(t)=(t,1-t,0) with ...
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4answers
134 views

Contour Integral help with residue theorem

$$ K = \int_{0}^{\infty}\frac{1}{x^{4}+x^{2}+1}dx $$ I am supposed to use contour integration to solve this, but I can't even determine the singularities. The denominator doesn't have any that I can ...
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0answers
156 views

Integrating over a closed contour following vector field

Integrate over a closed contour $c$ $$\oint_c d\vec{r}\times\vec{a}, \quad \vec{a}=-yz\vec{i}+xz\vec{j}+xy\vec{k}$$ where $c$ is cross-section of following two surfaces $$x^2+y^2+z^2=1$$ and $$y=x^2$$ ...