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Chapter 14: Q57P (page 702)

Find the inverse Laplace transform of the following functions by using (7.16). p+1p(p2+1)

Short Answer

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The residues at poles, f(t)=1+sint-cost

Step by step solution

01

To find the poles of    by denominator.

Using convolution of we have to find the inverse transform.

The given equation is,

Rewrite it equation as,

To find the poles of by denominator as,

Simple poles have the above equation, and

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Most popular questions from this chapter

w =鈭歾. Hint: This is equivalent to w2 = z; find x and y in terms of u and v and then solve the pair of equations for u and v in terms of x and y. Note that this is really the same problem as Problem 1 with the z and w planes interchanged.

Use the Cauchy-Riemann conditions to find out whether the functions in Problems 1.1 to 1.21 are analytic.

z炉

Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.

e3z-3z-1z4at z = 0

Find the residues of the following functions at the indicated points. Try to select the easiest of the methods outlined above. Check your results by computer.

z+2z2+9z2+1atz=3i

For each of the following functions w = f(z) = u +iv, find u and v as functions of x and y. Sketch the graph in (x,y) plane of the images of u = const. and v = const. for several values of and several values of as was done for in Figure 9.3. The curves u = const. should be orthogonal to the curves v = const.

w = ez
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