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Using laplace trasnform solve the following differential equation with given condition. (D2-2D+1) x=et, with x=2, Dx=-1, at t=0
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Find the analytic function f(z)= u+iv in terms of z if u-v=ex (cos y - sin y)
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Find inverse Z-transform of \[F(z)=\dfrac {z}{(z-1)(z-2)},|z|>2 \]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Verify Stoke's theorem for F=yzi + zxj+xy k and c is the boundary of the circel x2+y2+z2=1, z=0
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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108
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Find the bilinear transformation which maps the points 0, I, -2i of z-plane on to the points -4i, ?, 0 respectively of w-plane. Also obtain fixed points of the transformation
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Find inverse Laplace Transform of following \[\left(i\right)\ \log{\left(1+\frac{a^2}{s^2}\right)}\] \[\left(ii\right)\ \frac{s}{{\left(s+1\right)}^2\left(s^2+1\right)}\]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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For what value of ? the equations x+y+z=1, x+2y+4z=?, x+4y+10z=?2 have a solution and solve them completely in each case.
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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70
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Obtain complex form of Fourier series for the functions f(x)= eax in (0,a)
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Evaluate by Green's theorem \[\int_C^{\ }\ \left[\left(3x^2-8y^2\right)\ dx+\left(4y-6xy\right)\ dy\right]\] where C is the boundary of the region bounded by \[y=\sqrt{x},\ \ y=x^2\]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Find the inverse Laplace transform of ? \[ \left(i\right)\ \frac{e^{-2s}}{s^2+8s+25} \\ \left(ii\right)\ \frac{e^{-3s}}{{\left(s+4\right)}^3}\]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Find Laplace Transform of following \[\left(i\right)\ \int_0^1\frac{1-e^{-au}}{u}\ du\] \[\left(ii\right)\ \ {\left(t\sinh{2t}\right)}^2\]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Find the inverse Laplace transform of \[\frac{e^{-z^3}}{s^2-2s+2}\]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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124
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Find the Fourier series expansion for f(x)=|x|, in (-?, ?) Hence deduce that \[\frac{{\pi{}}^2}{8}=\frac{1}{1^2}+\frac{1}{3^2}+\frac{1}{5^2}...\]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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80
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(i) Find complex form of Fourier series for f(x) = cosh3x + sinh3x in (-π,π)
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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113
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Find Fourier series for f(x) = x + x2 in (-π , π) Hence deduce that \[ \dfrac{1}{1^2}+ \dfrac{1}{3^2}+ \dfrac{1}{5^2} +\frac{1}{7^2} +....= \dfrac{{\pi}^2}{8} \]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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113
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Find Z-transform of {k2 - 2k + 3}k ≥ 0
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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114
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Find the Fourier series of f(x) = cos μx in (-π,π), where μ is not an integer.
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Using laplace trasnform solve the following differential equation with given condition. (D2-3D+2) y=e2t, y(0)=-3, y'(0)=5
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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965
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Find the analytic function f(z)=u+iv in terms of z if u-v=(x-y) (x2 + 4xy + y2)
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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125
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Find inverse Laplace Transform of following (i) 2 tanh-1 s \[\left(ii\right)\frac{s^2}{\left(s^2+1\right)\left(s^2+4\right)}\]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Obtain complex form of Fourier series for the functions f(x)= sin a x in (-?, ?)
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Evaluate by Green's theorem \[\int_C\bar{F}\cdot{}d\bar{r}\ where\ \ \bar{F}=xy\left(xi-yi\right) \ and \ C \ is \ r=a(1+ \cos \theta) \]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Find Laplace Transform of following \[\left(i\right)\ e^{-4t}\ \int_0^1u\sin{3u\ du}\] \[\left(ii\right)\ \frac{1}{t}(1-\cos{t)}\]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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Find the Fourier series expnasion for \[ f(x)= \sqrt{1-\cos x} in (0,2?) \ Hence \ deduce \ that \ \sum_{n=1}^{\infty}\dfrac{1}{4n^2 -1}=\dfrac{1}{2} \]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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\[ if \ \int^{\infty}_{0}e^{-2t} \sin (t+\alpha) \cos (t-\alpha)dt=\dfrac {3}{8} \ then \ find\ \alpha \]
engineering mathematics updated 4 months ago by teamques10 ♣ 9.2k
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