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2020_1 NOUN TMA3 Questions & Answers: MTH381 - Mathematical Methods III

Posted: Mon Jun 01, 2020 12:34 am
by Jed
2020_1 NOUN TMA3 Questions & Answers: MTH381 - Mathematical Methods III





MTH381


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What is the Laplace transform of the function \\(f(t)=t\\) where \\(t\\geq 0\\).

\\(\\frac{1}{s^2}\\)


Given that \\(u=\\frac{yz}{x}\\), \\(v=\\frac{xz}{y}\\) and \\(w=\\frac{xy}{z}\\), then what is the value of \\(\\frac{\\partial(u, v, w)}{\\partial(x, y, z)}\\) ?

4


Find the Jacobian of p, q, r with respect to x, y, z given \\(p=x+y+z, q=y+z\\) and \\(r=z\\)

1

Evaluate the residue of \\(f(z)=\\frac{1+e^z}{sin z+z cos z}\\)at the pole where \\(z=0\\).

1


Find the pole of this function \\(f(z)=\\frac{z-2}{z^2}sin \\frac{1}{z-1}\\)

2



The Stoke’s theorem uses which of the following operation?

Curl



What is an integral curve along a simple closed curve called?

Countour Integral




The singularity of \\(f(z)=\\frac{z+3}{(z-1)(z-2)}\\) are

\\(z=1,2\\)





Find the \\(_{z\\rightarrow2+3i}lim[3x+i(2x-4y)]\\)

\\(6+16i\\)



Fourier series uses which domain representation of signals?

Frequency domain representation




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