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0
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1
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387
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1
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\[ if \ L[J_0 (t) ] = \dfrac {1}{\sqrt{s^2+1}} \] prove \[ \int^\infty_0 e^{-6t} t J_0 (4t) dt = 3/500 \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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646
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1
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If \[ \overline A = \nabla (xy+ yz+ zx), \ find \ \nabla\cdot \overline A \ and \ \nabla \times \overline A \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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584
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Using laplace transform solve the following differential equation with given condition \[ \dfrac {d^2y}{dt^2} +y=t, \] given taht y(0)=1&y'(0)=0.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
6
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40k
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Find the Fourier series expansion for f(x)=|x|, in (-π, π).
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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685
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Prove that f(z)=x2-y+2ixy is analytic and find f'(z).
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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358
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Prove that \[ \int xJ_{2/3} (x^{3/2})dx = - \dfrac {2}{3} x^{-1/2}J_{-1/3}(x^{3/2}) .\]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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650
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Define billinear transformation, And prove that in a general, a bilinear transformation maps a circle into a circle.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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502
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Using Gauss's Divergence theorem \( \iint_s \ \overline {F} .d\overline {s} \) where F2x2yi-y2j+4xz2 k and s is the region bounded by y2+z2=9 and x=2 in the first octant.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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528
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Find the Fourier series if f(x)=|x|, -k
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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794
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1
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Find the Fourier series if f(x)=|x|, -k
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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1
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762
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1
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Find the Fourier series if f(x)=|x|, -k
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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526
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Find inverse Laplace transform of the following: \[ i) \ \dfrac {S^2} {(S^2 + a^2) (S^2+b^2)} \\ ii) \ \dfrac {S+2}{S^2 -4S+13} \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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8.5k
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If v=ex sin y, prove that v is a Harmonic function. Also find the corresponding harmonic conjugate function and analytic function.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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539
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f f(x)=C1Q1(x) + C2Q2(x) + C3Q3(x)t where C1, C2, C3 constants and Q1, Q2, Q3 are orthonormal sets on (a,b), show that. \[ \int^b_a [f(x)]^2 dx = c^2_1 + c^2_2 + c^2_3. \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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410
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Find the Laplace transforms of the following. \[ i) \ e^{-t} \int^t_0 \dfrac {\sin u} {u} du \\ ii) \ t \sqrt{1+\sin t} \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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1.4k
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Verify Green's theorem in the plane for ∮(x2-y)dx+(2y2+x)dy Around the boundary of region defined by y=x2 and y=4.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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488
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Prove that \[ J_{1/2}(x) = \sqrt{ \dfrac {2} {\pi x } }\cdot \sin x \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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5.1k
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Find the Fourier series of the function f(x)=e-x. 0
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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6.8k
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Solve by using Laplace Transform. (D2+2D+5)y=e-t sin t, when y(0)=0, y(0)=1.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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391
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Evaluate by using Laplace Transformation \[ \int^\infty_0 e^{-3x} t \cos t \ dt. \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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965
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Determine the constants a,b,c,d if f(z)=x2+2axy+by2+i(dx2+2cky+y2) is analytic.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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2.2k
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Determine the constants a,b,c,d if f(z)=x2+2axy+by2+i(dx2+2cky+y2) is analytic.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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486
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Prove that the transformation \(w=\dfrac {1}{z+1}\) transforms the real axis of the z-plane into a circle in the w-plane.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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452
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Verify Green's Theorem for \(\int_c \overline{F} \cdot \overline {dr}\) where \( \overline {F}= (x^2 - y^2)\widehat {i} + (x+y)\widehat{j}\) and C is the triangle with vertices (0,0), (1,1) and (2,1).
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
0
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391
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Using Convolution theorem find \[ L^{-1} \left [ \dfrac {s^2}{(s^2+4)^2} \right ] \]
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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