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Evaluate $\int\int\limits_{s} (\nabla \times \overline{F}ds$ where $\overline{F} = (2x - y + z)i + (x + y - z^2)j + (3x - 2y + 4z)k$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find a, b , c if $\overline{F}=(axy+bz^3) \overline{i} + (3x^2 -cz) \overline{j} + (3xz^2 -y)\overline{k}$ is irrotational.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Using Green Theorem evaluate $\int\limits_{c} (xy + y^2)dx + x^2 y$ where c is the closed surface bounded by y = x and $y = x^2$.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Show that a closed curve 'C' of given fixed length (perimeter) which enclosed maximum area is a circle.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Evaluate by using Residue theorem $\int\limits_{0}^{2\pi} \frac{d\theta}{(2 + cos\theta)^2}$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Evaluate $\int\limits_{-\infty}^{\infty} \frac{cos3x}{(x^2 + 1)(x^2 + 4)}dx$ using Cauchy Residue Theorem
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Evaluate $\int\limits_{c} |z| dz$, where c is the left half of unit circle $|z| = 1$ from z = -i to z = i
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Obtain two distinct Lament's series expansions of $f(z) = \frac{2z - 3}{z^2 - 4z + 3}$ in powers of (z - 4) indicating region of convergence in each case.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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$f(a) = \int\limits_{c} \frac{3z^2 + 7z + 1}{z - a}dz$ where c is a circle $|z| = 2$. Find the value of 1) f(-3) 2) f(i) 3) f'(1 - i) 4) f"(1 - i)
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Evaluate $\int \frac{dz}{z^3(z + 4)}$ where $|z| = 4$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find expansion of $f(z) = \frac{1}{(1 + z^2) (z + 2)}$ indicating region of convergence.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Using Cauchy's Residue Theorem evaluate $\int\limits_{\infty}^{\infty} \frac{x^2}{x^6 + 1}dx$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Evaluate $\int\limits_{0}^{1 + i} (x^2 + iy)dz$ along y = x and $y = x^2$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Evaluate $\int\limits_{0}^{\infty} \frac{x^3 sinx}{(x^2 + a^2)^2}dx$ using contour integration
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find f(3), f'(1 + i), f"(1 - i) if $f(a) = \oint \frac{3z^2 + 11z + 7}{z - a}dz,$ c: |z| = 2.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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If $\phi(\alpha) = \oint \frac{ze^z}{z - \alpha}dz$ where c is |z - 2i| = 3 find $\Phi(1), \Phi'(2), \Phi(3), \Phi'(4)$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Obtain Taylor's series and two distinct Laurent's series expansion of $f(z) = \frac{z - 1}{z^2 - 2z - 3}$ about z = 0, indicating region of convergence.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find the Eigen values and Eigen vectors for the matrix $\begin{bmatrix} 2 & 2 & 1 \\ 1 & 3 & 1 \\ 1 & 2 & 2 \end{bmatrix}$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Show that the matrix $A = \begin{bmatrix} 7 & 4 & -1 \\ 4 & 7 & -1 \\ -4 & -4 & 4 \end{bmatrix}$ is derogatory and find its minimal polynomial.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find the approximate value of $\int\limits_0^6e^x \space dx\space dy$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find the area using double integration where the region of integration is bounded by the curves $axy=4$ and $2x+y=2$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find the perimeter of the cardiode $r=(1+\cos \theta)$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find the singular value decomposition of the following matrix $\begin{bmatrix} 1 & 2 \\ 1 & 2 \end{bmatrix}$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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If A=$ \left[ \begin{array}{ccc} 3/2 & 1/2 \\ 1/2 & 3/2 \end{array}\right] $ , then find $e^A$ and $4^A$ with the help of modal matrix.
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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Find the eigen values and eigen vectors of matrix A = $\begin{bmatrix} -2 & 5 & 4 \\ 5 & 7 & 5 \\ 4 & 5 & -2 \end{bmatrix}$
engineering mathematics updated 3.8 years ago by krithikkm200 • 10
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