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Verify Stoke's theorem for \[\bar{F}=x^2\bar{i}+xy\bar{j}\] & C is the boundary of the rectangle x=0, x=2, y=3.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find inverse z-transform of F(z)= 1/(z-2)(z-3) if ROC is 2 < |z| < 3.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Using Lapace transform solve the differential equation \[\frac{d^2y}{{dt}^2}-2\frac{dy}{dt}-8y=4\ ,\ y\left(0\right)=0,\ y^{'}\left(0\right)=1.\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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645
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Find the Bilinear Transformation which maps the points 2,i,-2 on the points 1,i,-1
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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650
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Find the analytic function f(z)=u+iv if u=(r+ a2/r) cos ?.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the Laplace transform of f(t) = 1, 0 ? t ?a f(t) =1, a < t ? 2a & f(t + 2a)= f(t)
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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if A= \[\left[\begin{array}{ccc}1 & 1 & 1 \\2 & 5 & 7 \\2 & 1 & -1\end{array}\right]\] compute A l and hence, Solve the system of equation x + y + z = 9, 2x + 5y + 7z =52, 2x + y - z = 0.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Obtain Complex form of Fourier series for f(x)=e-ax in (-2,2)where a is not an integer.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Verify Green's Theorem in the plane for ?c (xy+y2) dx+x2 by where c is a closed curve of a region bounded by y=x and y2=x
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find inverse Laplace transform of (I) log (s-2/s-3) (II) s+1/s2 - 4
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the Fourier expansion of f(x)=cospx where p is not an integer in (0,2?)
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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537
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Using Laplace Transform evaluate \[\int_0^{\infty{}}e^{-t}\frac{\sin{3t}}{t}dt.\ \ \ \ \ \ \ \ \ \ \ \ \ \ \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Find the Laplace Transform of t? \[\sqrt{1+sint}\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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680
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Find the Fourier Expansion of f(x)=sinx in (-?,?).
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Show that \[ f(z)=\frac{\bar{z}}{{\left\vert{}z\right\vert{}}^2} \ \ \ \ \ \ , |z|?0 \] is analytic function.Hence find f'(z)
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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428
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Prove that \[\intJ_3\left(x\right)dx=\ -\frac{2J_1(x)}{x}-J_2(x)\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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572
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Show that the function V=ex (xsiny+ycosy) satisfies Laplace equation and find its corresponding analytic function
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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445
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Find Inverse Laplace Transform of? \[i)log\left(\frac{s^2+4}{s^2+9}\right)\] \[ii)\frac{s}{\left(s^2+4\right)\left(s^2+9\right)}\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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528
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Show that the set of functions {sin??x,sin??3x?} OR {sin??(2n+1)x:n=0,1,2,3} is orthogonal over [0,??2],Hence construct orthonormal set of functions.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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491
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i) Find the Laplace Transform of \[\frac{\cos{bt-\cos{at}}}{t}\] ii) Find the Laplace Transform of \[\frac{d}{dt}\left[\frac{sint}{t}\right].\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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Evaluate by Green's theorem \[\oint_c\left(x^2ydx+y^3dy\right)\] where c is closed path formed by y=x,y=x2
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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463
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Prove that \[J_{\frac{3}{2}}=\sqrt{\frac{2}{\pi{}x}}.\left(\frac{\sinx}{x}-\cosx\right)\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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483
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Find the Fourier expansion of \[f(x)=\sqrt{1-cosx}\ in\left(0,2\pi{}\right).Hence\ prove\\frac{1}{2}=\sum_{n=1}^{\infty{}}\frac{1}{4n^2-1}.\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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687
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Find the directional derivative of d=x2 y cos?z at (1,2, ?/2)in the direction of t=2i + 3j + 2k.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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628
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Using laplace transofrm solve- (D2 + 3D + 2) y= e-2t. Sin t where y(0) = 0 and y' (0) =0.
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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