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\[If\ \ \vec{F}=xye^{2z}i+xy^2coszj\ \ \ +x^2cosxyk.Then\ find\ div\ \bar{F\ }and\curl\ \bar{F.}\]\[\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the Laplace Transform of \[\int_0^t\ {ue}^{-3u}\sin{4udu}\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the fourier series for f(x)=|sin x| in (-?,?).
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Prove that real and imaginary parts of an analytic function F(z)=u+iv are harmonic function.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the bilinear transformation which maps the points z=1, I, -1 onto w=0, 1, ?
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Using convolution theorem; evaluate \[L^{-1}\left\{\frac{1}{\left(S-1\right)\left(s^24\right)}\right\}\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Verify Green's theorem, for \[\oint_C\left(3x^2-8y^2\right)dx+\left(4y-6xy\right)\] by where c is boundary of the region defined by x=0, y=0, and x+y=1
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find inverse Laplace transform of :- \[\left(i\right)\frac{1}{s}{\tan h}^{-1}{\left(s\right)}\] \[\left(ii\right)\ \frac{se^{-2s}}{\left(s^2+2s+2\right)}\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find Laplace transform of (i) te-3t cos2t.cos3t (ii) \[\frac{d}{dt}\left[\frac{\sin{3t}}{t}\right]\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the analytic function f(z)= u+iv where u=r2 cos2θ-r cosθ+2
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Obtain the fourier series of f(x) given by \[f\left(x\right)=\left\{\begin{array}{l}0,\ \ \&-\pi{}\leq{}x\leq{}0 \\x^2,\ \ \&0\leq{}x\leq{}\pi{}\end{array}\right.\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Evaluate \[\frac{d^2y}{dt^2}+2\frac{dy}{dt}-3y=sint,\] y(0)=0, y'(0)=0, by Laplace transform
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Obtain complex form of fourier series for f(x)= eax in (-1, 1)
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the bilinear transformation, which maps the points z=1,1,? onto the points w=-i, -1, i.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Evaluate by Stoke's theorem \[ \int_c (xy \ dx + x y^2 \ dy) \] where C is the square in the xy-plane with vertices (1,0), (0,1), (-1,0) and (0,-1).
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Show that the function u=sin x cosh y+2 cos x sinh y+ x2-y2+4xy satisfies Laplace's equation and find it corresponding analytic function.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Prove that \[ \overline{F} = \dfrac {\overline r}{r^3} \] is both irrotational and solenoidal.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find inverse Laplace Transform of following \[ i) \ \log \left [\dfrac {s^2+a^2}{\sqrt{s+b}} \right ] \\ ii) \ \dfrac {1}{s^3 (s-1)} \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the analytic function whose imaginary part is \[ v=\dfrac {x}{x^2+y^2} + \cos h \ y\cdot \cos x\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Obtain complex form of Fourier series for the function f(x)=sin ax in (-?, ?), where a is not an integer.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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i) Find Laplace Transform of \[ e^{-\pi} \int^t_c u \sin 3u \ du ii) Find Laplace Transform of \[ \dfrac {d}{dt} \left ( \dfrac {1-\cos 2t}{t} \right )
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Using Green's theorm evaluate \[ int_c (2x^2-y^2)dx + (x^2+y^2) dy where 'c' is the boundary of the surface enclosed by the line x=0, y=0, x=2, y=2.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Prove that \[ J_{1/2}(x) = \sqrt{\dfrac {2}{\pi x}} \sin x \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the Fourier series expansion for f(x)=4-x2, in (0,2) Hence deduce that \[ \dfrac {\pi^2}{6}=\dfrac {1}{1^2} + \dfrac {1}{2^2}+ \dfrac {1}{3^2} \cdots \ \cdots \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the directional derivative of &straighthi=x4+y4+z4 at (1,-2,1) in the direction of AB where B is (2,6,-1). Also find the maximum directional of ϕ at (1,-2,1).
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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