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1
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609
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1
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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 4.9 years ago by teamques10 ★ 70k
5
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24k
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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 4.9 years ago by teamques10 ★ 70k
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530
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1
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Find inverse Z-transform of \[F(z)=\dfrac {z}{(z-1)(z-2)},|z|>2 \]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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1
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1.1k
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1
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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 4.9 years ago by teamques10 ★ 70k
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2.1k
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1
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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 4.9 years ago by teamques10 ★ 70k
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1.6k
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Prove that u=e3 cos y+x3 - 3xy2 is harmonic
engineering physics updated 4.9 years ago by teamques10 ★ 70k
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654
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1
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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 4.9 years ago by teamques10 ★ 70k
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757
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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 4.9 years ago by teamques10 ★ 70k
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673
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1
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Obtain complex form of Fourier series for the functions f(x)= eax in (0,a)
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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1
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831
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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 4.9 years ago by teamques10 ★ 70k
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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 4.9 years ago by teamques10 ★ 70k
0
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1
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553
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1
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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 4.9 years ago by teamques10 ★ 70k
0
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1
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379
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1
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\[If\ \left\{\ f\left(k\right)\right\}=\left\{\ 2^0,2^1,\ 2^3,...\right\}\] Find Z{ f(k) }
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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476
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1
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Find the inverse Laplace transform of \[\frac{e^{-z^3}}{s^2-2s+2}\]
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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2.8k
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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 4.9 years ago by teamques10 ★ 70k
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3.3k
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Prove that f(z)=(x3-3xy2+2xy) + i(3x2y-x2+y2-y3) is analytic and find f'(z) & f(z) in terms of z
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
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1.4k
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1
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(i) Find complex form of Fourier series for f(x) = cosh3x + sinh3x in (-π,π)
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
2
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1
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2.0k
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1
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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 4.9 years ago by teamques10 ★ 70k
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1
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4.2k
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1
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Find Z-transform of {k2 - 2k + 3}k ≥ 0
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
0
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1
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3.2k
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1
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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 4.9 years ago by teamques10 ★ 70k
0
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1
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588
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1
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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 4.9 years ago by teamques10 ★ 70k
3
votes
1
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22k
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1
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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 4.9 years ago by teamques10 ★ 70k
0
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1
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3.9k
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1
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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 4.9 years ago by teamques10 ★ 70k
0
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1
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633
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1
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Obtain complex form of Fourier series for the functions f(x)= sin a x in (-?, ?)
engineering mathematics updated 4.9 years ago by teamques10 ★ 70k
0
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1
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748
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1
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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 4.9 years ago by teamques10 ★ 70k
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