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Engineering Mathematics

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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 5.7 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 5.7 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 5.7 years ago by teamques10 ★ 70k
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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 5.7 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 5.7 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 5.7 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 5.7 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 5.7 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 5.7 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 5.7 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 5.7 years ago by teamques10 ★ 70k
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If $u=x^2-y^2 \; , \; v=2xy \; and \; z=f(u,v) $ prove the following
engineering mathematics updated 5.7 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 5.7 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 5.7 years ago by teamques10 ★ 70k
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Find the values of $\lambda$ for which the following equations have a solution and solve them completely for each value of $\lambda $ .
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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what values of $\lambda$, system of equations have a non-trivial solution? Obtain solution for real values of $\lambda$ where $3x+y-\lambda z=0 \; ; 4x-2y-3z=0 \; ; 2\lambda +4y-\lambda z =0$
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Determine the values of $\lambda $ so that the equations $x+y+z=1 \; ; \; x+2y+4z=\lambda \; ; \; x+4y+10z=\lambda^2$ have solution and solve them completely in each case.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Reduce the matrix A to normal form and hence find its rank where $ A \;=\;\left[ \begin{array}{cccc}0& 1& -3& -1\\1& 0& 4& 3\\3& 1& 0& 2 \\1& 1& -2& 0\end{array}\right] $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Test the consistency of the following equations and solve them if they are consistent $ \\ \; \\ 2x-y+z=8 \; , \; 3x-y+z=6 \;, \; 4x-y+2z=7 \;, \; -x+y-z=4 $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Reduce the matrix A to normal form and hence find its rank where $ \left[ \begin{array}{cccc}1&-1& 3& 6\\1& 3&-3 &-4\\5& 3 & 3 & 11\end{array}\right] $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Prove that $sinh \; x \; = \; x+\dfrac{x^3}{3!}+\dfrac{x^5}{5!}+\dfrac{x^7}{7!}+\ldots $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Show that every square matrix can be uniquely expressed as the sum of Hermitian and skew Hermitian matrix.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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If 'A' is Skew Symmetric matrix of odd order, then prove that it is singular.
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Find two non-singular matrices P & Q such that PAQ is in normal form where$ A= \left[ \begin{array}{cccc} 1 & 2 & 3 & -4 \\ 2 & 1 & 4 & -5 \\ -1 & -5 & -5 & 7 \end{array}\right]$ Also find rank of A
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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Reduce matrix A to normal form and find its rank where $A=\left[ \begin{array}{cccc} 1 & 2 & 3 & 2 \\ 2 & 3 & 5 & 1 \\ 1 & 3 & 4 & 5 \end{array} \right] $
engineering mathematics updated 5.7 years ago by teamques10 ★ 70k
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