Advanced Engineering Mathematics, 7th Edition

19 Chapter in Review Answers to selected odd-numbered problems begin on page ANS-48.

Answer Problems 1–12 without referring back to the text. Fill in the blank or answer true/false.

1. A function f is analytic at a point z₀ if f can be expanded in a convergent power series centered at z₀. _____
2. A power series represents a continuous function at every point within and on its circle of convergence. _____
3. For f(z) = 1/(z − 3), the Laurent series valid for |z| > 3 is z⁻¹ + 3z⁻² + 9z⁻³ + … . Since there are an infinite number of negative powers of z = z − 0, z = 0 is an essential singularity. _____
4. The only possible singularities of a rational function are poles. _____
5. The function f(z) = e^1/(z−1) has an essential singularity at z = 1. _____
6. The ...