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

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

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 Stokeâ€™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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