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5
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1
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15k
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1
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Show that under the transformation w = (5 - 4z)/(4z - 2) the circle |z| = 1 in the z plane is transformed into a circle of unity in the W plane.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
1
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1
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4.0k
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1
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Evaluate $\int J_{3}(x)dx$ and express the result in terms of $J_{0}$ and $J_{1}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
3
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1
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23k
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1
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Show that the function $v = e^x (xsiny + ycosy)$ satisfies Laplace equation. Find its corresponding analytic function & its harmonic conjugate.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.5k
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1
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Show that $J_{\frac{5}{2}} = \sqrt{\frac{2}{\pi x}}\bigg[\frac{3 - x^2}{x^2}sinx - \frac{3}{2}cosx \bigg]$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
3
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1
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12k
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1
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Find the imaginary part whose real part is $u = x^3 - 3xy^2 + 3x^2 - 3y^2 + 1$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.9k
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1
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Prove that $\int J_{3}(x)dx = \frac{-2J_{1}(x)}{x} - J_{2}(x)$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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24k
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1
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Prove that real and imaginary parts of an analytic function f(z) = u + iv are harmonic function.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
3
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1
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20k
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1
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Using Gauss divergence theorem evaluate $\int\limits_{C}\bar{F} \cdot \overline{ds}$ where $F = 2x^2yi - y^2j + 4xz^2k$ and S is the region bounded by $y^2 + z^2 = 9$ and x = 2 in the first octant.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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4.5k
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1
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Verify green's theorem in the plane for $\oint\limits_{s} (x^2 - y)dx + (2y^2 + x)dy$ around the boundary of region defined by $y = x^2$ and y = 4
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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2.5k
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1
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Evaluate by stoke's theorem $\int\limits_{C}xydx + xy^2 dy$ where C is the square in the xy plane with vertices (1,0), (0,1), (-1,0) and (0,1)
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.7k
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1
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Using Green's theorem evaluate $\int\limits_{c}(2x^2 - y^2) + (x^2 - y^2)dy$ where c is the boundary of the surface enclosed by the lines x = 0, y = 0, x = 2, y = 2
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
1
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1
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14k
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1
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Define Solenoidal vector. Hence prove that $\bar{F} = \frac{\bar{a} \times \bar{r}}{r^n}$ is a solenoidal vector.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
3
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1
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27k
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1
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A vector field is given by $\bar{F} = (x^2 + xy^2)i + (y^2 + x^2 y)j$. Show that $\bar{F}$ is irrotational and find its scalar potential such that $\bar{F} = \bar{V}\phi$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
1
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1
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7.2k
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1
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Find the directional derivative of $\phi = x^4 + y^4 + z^4$ at A(1,-2,1) in the direction of AB where B is (2,6,-1). Also find the maximum directional derivative of $\phi$ at (1,-2,1)
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
3
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1
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25k
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1
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Prove that $\bar{F} = \frac{r}{r^3}$ is both irrotational and solenoidal.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.4k
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1
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If $\bar{A} = \bar{V}(xy + yz + zx)$ find $\bar{V}\cdot \bar{A}$ and $\bar{V} \times \bar{A}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.3k
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1
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Evaluate following using appropriate theorem $\int\int\limits_{s}(9x\bar{i} + 6y\bar{j} - 10z\bar{k})$ where s is the surface of sphere with radius 2 units.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.5k
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1
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Evaluate the following by using appropriate theorem $\int Fdr$ where $\bar{F} = (2x - y)\hat{i} - (yz^2)\hat{j} - (y^2 z)\hat{k}$ and c is the boundary of upper half of sphere $(x^2 + y^2 + z^2) = 4$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
1
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1
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21k
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1
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Prove that the angle between two surface $x^2 + y^2 + z^2 = 9$ and $x^2 + y^2 - z = 3$ at the point (2, -1, 2) is $cos^{-1}\bigg(\frac{8}{3\sqrt{21}}\bigg)$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
2
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1
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46k
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1
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Find the constants a,b,c so that $\bar{F} = (x + 2y + az)\hat{i} + (bx - 3y - z)\hat{j} + (4x + cy + 2z)\hat{k}$ is irrotational
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
1
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1
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2.6k
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1
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Find the work done in moving a particle in a force field given by $\bar{F} = 3xy\hat{i} - 5z\hat{j} + 10x\hat{k}$ along the cirlce $x = t^2 + 1, y = 2t^2, z = t^3$ from t = 1 to t = 2
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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10.0k
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1
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A vector field $\bar{F}$ is given by $\bar{F} = (x^2 - yz)\hat{i} + (y^2 - zx)\hat{j} + (z^2 - xy)\hat{k}$ is irrotational and hence find scalar point function $\phi$ such that $\bar{F} = \bar{V}\phi$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.3k
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1
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Evaluate by green's theorem $\oint\limits_{c} (x^2 yax + y^3)dy$ where C is closed path formed by y = x, y = $x^2$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.4k
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1
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Find the directional derivative of d = $x^2 ycosz$ at $(1,2,\frac{\pi}{2})$ in the direction of $\bar{a} = 2\bar{i} + 3\bar{j} + 3\bar{k}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
0
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1
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1.2k
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1
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If $\bar{F} = xye^{2x}\bar{i} + xy^2 cosz\bar{j} + x^2 cosy\bar{k}$ find div $\bar{F}$ & curl $\bar{F}$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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