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1
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2.7k
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1
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Jacobians : If $ u=1-x , \; v=x(1-y) , \; w = xy(1-z) \; , \; Show \; that \; \frac{\partial (u,v,w) }{\partial (x,y,z)} \; = \; -x^2y $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $ x = rcos\theta \; y=rsin\theta. \; Find \frac{\partial (x,y) }{\partial (r,\theta)} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
8
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Jacobians : If $ u = \frac{x+y}{1-xy} , \; v \; = \; tan^{-1}x \; + \; tan^{-1}y , \; Find \frac{\partial (u,v)}{\partial (x,y)} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Jacobians : If $ x=e^v sec \; u \; , \; y=e^v tan \; u, Find \; J\bigg ( \frac{u,v}{x,y} \bigg) $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $U=xyz, V=x^2+y^2+z^2, W=x+y+z $ Then prove that $\dfrac {dx}{dU}=\dfrac 1{(x-y)(x-z)}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $x=r\sin \theta\cos\phi,y=r\sin\theta\sin\phi z=r\cos \theta $ then find $\dfrac {d(r,\theta\phi)}{d(x,y,z)}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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State and prove Euler's theorem for three variables and hence find the following
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Euler Theorem : If $ x+y=2e^{\theta} cos\phi \;, \; \; x - y \;=\; 2ie^{\theta} sin\phi \; \;$and u is a function of $x$ and $y$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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State and prove Euler theorem for a homogeneous function in two variables and hence find $x\dfrac{\partial u}{\partial x}+y\dfrac{\partial u}{\partial y} \; if\;u=\dfrac{\sqrt{xy}}{\sqrt{x}+\sqrt{y}}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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State and prove Euler theorem for a homogeneous function in two variables and hence find the value of following :
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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State and prove Euler theorem for a homogeneous function in two variables and find $ x\dfrac{\partial u}{\partial x}+y\dfrac{\partial u}{\partial y} \;\; where\;u=\dfrac{\sqrt{x}+\sqrt{y}}{x+y} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $u \; = \; tan^{-1} (\frac{y}{x}), \; find \; \frac{\partial^2 u}{\partial x^2} \; + \frac{\partial^2 u}{\partial y^2}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $x$ = $cos\theta \; - \; r sin\theta$ , y = $sin\theta \; + \; r cos\theta \\ \; \\ Prove \ that \ \frac{\partial r}{\partial x} \; = \; \frac{x}{ r} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Basic partial derivatives : u = $x^2y$ + $e^{xy^2}$, Show that $ \frac{\partial^2 \; u}{\partial x \partial y} \; = \; \frac{\partial^2 \; u}{\partial y \partial x} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
2
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Basic partial derivatives : u = log( $x^2$ + $y^2$ ), prove $ \frac{\partial^2 \; u}{\partial x \partial y} \; = \; \frac{\partial^2 \; u}{\partial y \partial x} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Basic partial derivatives : u = log( tan $x$ + tan y ). Prove : $ sin \; 2x \; \frac{\partial u}{\partial x} \; + \; sin \;2y \; \frac{\partial u}{\partial y} = 2 $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $z=\log(\tan x+\tan y) $ then prove that $\sin 2\dfrac {dz}{dx}+\sin 2y \dfrac {dz}{dy}=2.$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $ z=f(x,y)\;, x=e^u+e^{-v} \;, x=e^{-u}-e^{v} $prove that $\dfrac{\partial z}{\partial u} - \dfrac{\partial z}{\partial v}= x\dfrac{\partial z}{\partial x} - y\dfrac{\partial z}{\partial y} $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $ \dfrac{x^2}{1+u}+\dfrac{y^2}{2+u}+\dfrac{z^2}{3+u}=1 $ then prove the following
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $ u=sin(x^2+y^2)$ and $a^2x^2+b^2y^2=c^2$ , find $\dfrac{\partial u}{\partial z}$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $ u \;=\; f \bigg( \dfrac{x-y}{xy} , \dfrac{z-x}{xz} \bigg) $ prove the following
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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If $ u=f(x-y,y-z,z-x) , $ then show that $ \dfrac{\partial u}{\partial x} + \dfrac{\partial u}{\partial y} + \dfrac{\partial u}{\partial z} \;=\; 0 $
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
2
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44k
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If $u=x^2-y^2 \; , \; v=2xy \; and \; z=f(u,v) $ prove the following
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Solve the following system of linear equations by Crout's method x-y+2z=2 , 3x+2y-3z=2 , 4x-4y+2z=2
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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Solve the following system of equations : $2x-2y-5z=0, \; 4x-y+z=0, \; 3x-2y+3z=0, \; x-3y+7z=0$
engineering mathematics updated 6.0 years ago by teamques10 ★ 70k
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