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Engineering Mathematics A foundation for Electronic, Electrical, Communications and Systems Engineers

565 SOLVED PROBLEMS

Question: 24.14

Find, if possible, (a) the Laplace transform (b) the Fourier transform of f (t ) = u(t ) e^3t . Comment upon the result. ...

Question: 4.11

Show that R = √x² + y² + z² ...

Question: 4.12

Describe the surface R = 4. ...

Question: 9.7

If z1 = 2 − 2j and z2 = 3 + 4j, find z1z2. ...

Question: 29.20

The continuous random variable x has a standard normal distribution. Calculate the probability that (a) x 1.2 (c) x > −1.2 (d) x < −1.2 ...

Question: 24.13

Find F{sin at}. ...

Question: 24.12

Given that F{δ(t − a)} = e^−jωa find F{e^−jta}. ...

Question: 24.11

Apply the t-ω duality principle to the previous result. Interpret the result physically. ...

Question: 24.10

Use the properties of the delta function to deduce its Fourier transform. ...

Question: 24.9

Given that the Fourier transform of u(t) e^−t is 1/1 + jω use the duality principle to deduce the transform of 1/1 + jt. ...

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