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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

Expert verified

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

A fluid flow is called irrotational if ∇×V = 0 where V = velocity of fluid (Chapter 6, Section 11); then V = ∇Φ. Use Problem 10.15 of Chapter 6 to show that if the fluid is incompressible, the Φ satisfies Laplace’s equation. (Caution: In Chapter 6, we used V = vρ, with v = velocity; here V = velocity.)

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

|z|

Find out whether infinity is a regular point, an essential singularity, or a pole (and if a pole, of what order) for each of the following functions. Find the residue of each function at infinity,4z3+2z+3z2

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Evaluate the following integrals by computing residues at infinity. Check your answers by computing residues at all the finite poles. (It is understood that ∮ means in the positive direction.)

∮1-z21+z2dzzaround |z|=2
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