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Engineering Mathematics

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\[A=\frac{1}{7}\ \left[\begin{array}{ccc}2 & 6 & 3 \\6 & -3 & 2 \\3 & 2 & -6\end{array}\right]\] Show that- (i) |A| = 1 (ii) .adj A=A'
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Show that the Fourier cosine transform of- \[f\left(x\right)=\ \frac{1}{\sqrt{x}}\ is\ \frac{1}{\sqrt{s}}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Investigate for what value of ? and ? the equations. x+2y+3z=4, x+3y+4z=5, x+3y+?z= ? have (I) no solution (II) a unique solution (III) an infinite no. of solutions.
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Obtain half range cosine series for f(x)=sin(?x/l) in 0
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Show that under the transformation \[ w= \dfrac {5-4Z}{4z-2}\] the circle |z|=1 in the z-plane is transformed into a circle of unity in the w-plane. Also find the center of the circle
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Find L.T. of \[f\left(t\right)=\ f\left(x\right)= \Bigg\{\begin{align*}{}1,\ \ \ \ \ 0<t<a \\-1,\ \ \ \ a<t<2a\end{align*} \] And f(t) = f(t+2a)
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Find the relation of linear dependence amongst the rows of the matrix \[A=\left[\begin{array}{ccc}1 & 1 & -1 & 1 \\1 & -1 & 2 & -1 \\3 & 1 & 0 & 1\end{array}\right]\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Solve by using L.T. \[ \dfrac {dy}{dt}+2y+\int^{t}_{0}y \ dt=\sin t \ when \ y \ (0)=1\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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\[ Find L \ \left\{\frac{1-cost}{t^2}\right\} \]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Find : - L(sin2t cost cosh2t)
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Evaluate \[\int_0^{\infty{}}e^{-2t}\sinh{t\frac{\sin t}{t}}\ dt\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Using Fourier Cosine integral prove that \[e^{-x}\cos{x=\frac{2}{\pi{}}\\int_0^{\infty{}}\frac{\left({\omega{}}^2+2\right)}{\left({\omega{}}^4+4\right)}.\\cos{\omega{}\ x\ d\omega{}}}\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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"Find the domain response using graphical & partial fraction method & prove that results are matching \[F \left(S\right)=\frac{3s}{\left(s+6\right)\left(s+2\right)}\]"
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Show that the general solution of \[ \dfrac {d^2 y }{d x^2} + 4x^2 y=0 \ is \ y=\sqrt{z} [A J_{1/4} (x^2) + B \ J_{-1/4} (x^2)] \] where A and B are constants.
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Find non-singular matrices P & Q s.t. PAQ is in Normal form. Also find rank of A & A-1 \[A=\left[\begin{array}{ccc}1 & 3 & 3 \\1 & 4 & 3 \\1 & 3 & 4\end{array}\right]\]
engineering mathematics updated 4.6 years ago by vyshnavitorlako909 • 10
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If lambda is eigen value of A then prove that (lambda)^n is eigen value of A^n
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Verify Cayley Hamilton theorem for the matrix A and hence ,find $A^{-1}$ & $A^4$ ,where $A = \begin{bmatrix} \ 1 & 2 & -2 \\ \ -1 & 3 & 0 \\ \ 0 & -2 & 1 \\ \end{bmatrix}$
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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\[{(i) Find L^{-1}\left\{{tan}^{-1}{\left(s+2\right)}^2\right\} } \\ {(ii) Find L\left\{t^2H\left(t-2\right)-cos h t\ \delta{}\left(t-4\right)\right\}} \]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Evaluate by using L.T. \[\int_0^{\infty{}}{t^3e}^{-t}\ \ sin\ t\ dt\]
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Derive the equation for Laplace transform of following functions : (i) Unit Ramp function Unit impulse function
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Solve the $[D^4-4D^3+8D^2-8D+4]y=0$
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Explain fuzzy membership functions
engineering mathematics updated 4.6 years ago by pg1118329 • 0
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Using Lagrange's method of multipliers solve the NLPP, optimize $z = 4x_{1} + 8x_{2} - x_{1}^2 - x_{2}^2$ subjected to $x_{1} + x_{2} = 4, x_{1}, x_{2} \geq 0$.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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$\oint \frac{e^{2z}}{(Z+1)^4}dz$ where c is the circle |z-1|=3.
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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Evaluate $\int\int\limits_R e^{2x+3y}dxdy$ over the triangle bounded by $x+y=1 , x=0 , y=0$
engineering mathematics updated 4.6 years ago by teamques10 ★ 70k
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