Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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16.4. Show that if z' is the principal value, then
1+e**
z'dz =
(1-i),
2
where is the upper semicircle from z = 1 to z = -1.
L
16.8. For each of the following functions f, describe the domain of ana-
lyticity and apply the Cauchy-Goursat Theorem to show that f(z)dz =
0, where is the circle |2|=1:1
(a). f(z) =
1
z 2 + 2x + 2
(b). f(z) = ze*.
What about (c). f(z) = (2z-i)-2?
Chapter 5 Solutions
Advanced Engineering Mathematics
Ch. 5.1 - WRITING AND LITERATURE PROJECT. Power Series in...Ch. 5.1 - Determine the radius of convergence. Show the...Ch. 5.1 - Determine the radius of convergence. Show the...Ch. 5.1 - Determine the radius of convergence. Show the...Ch. 5.1 - Determine the radius of convergence. Show the...Ch. 5.1 - Apply the power series method. Do this by hand,...Ch. 5.1 - Apply the power series method. Do this by hand,...Ch. 5.1 - Apply the power series method. Do this by hand,...Ch. 5.1 - Apply the power series method. Do this by hand,...Ch. 5.1 - Find a power series solution in powers of x. Show...
Ch. 5.1 - Find a power series solution in powers of x. Show...Ch. 5.1 - Find a power series solution in powers of x. Show...Ch. 5.1 - Find a power series solution in powers of x. Show...Ch. 5.1 - Find a power series solution in powers of x. Show...Ch. 5.1 - Prob. 15PCh. 5.1 - Prob. 16PCh. 5.1 - CAS PROBLEMS. IVPs
Solve the initial value problem...Ch. 5.1 - Prob. 18PCh. 5.1 - Prob. 19PCh. 5.2 - Legendre functions for n = 0. Show that (6) with n...Ch. 5.2 - Legendre functions for n = 1. Show that (7) with n...Ch. 5.2 - Special n. Derive (11′) from (11).
Ch. 5.2 - Prob. 4PCh. 5.2 - Obtain P6 and P7.
Ch. 5.2 - Prob. 11PCh. 5.2 - Prob. 12PCh. 5.2 - Rodrigues’s formula. Obtain (11′) from (13).
Ch. 5.2 - Prob. 14PCh. 5.2 - Prob. 15PCh. 5.3 - Prob. 1PCh. 5.3 - Prob. 2PCh. 5.3 - Prob. 3PCh. 5.3 - Prob. 4PCh. 5.3 - Prob. 5PCh. 5.3 - Prob. 6PCh. 5.3 - Prob. 7PCh. 5.3 - Prob. 8PCh. 5.3 - Prob. 9PCh. 5.3 - Prob. 10PCh. 5.3 - Find a basis of solutions by the Frobenius method....Ch. 5.3 - Find a basis of solutions by the Frobenius method....Ch. 5.3 - Find a general solution in terms of hypergeometric...Ch. 5.3 - Find a general solution in terms of hypergeometric...Ch. 5.3 - Find a general solution in terms of hypergeometric...Ch. 5.3 - Find a general solution in terms of hypergeometric...Ch. 5.3 - Find a general solution in terms of hypergeometric...Ch. 5.3 - Find a general solution in terms of hypergeometric...Ch. 5.4 - Prob. 1PCh. 5.4 - Prob. 2PCh. 5.4 - Prob. 3PCh. 5.4 - Prob. 4PCh. 5.4 - Prob. 5PCh. 5.4 - Prob. 6PCh. 5.4 - Prob. 7PCh. 5.4 - Prob. 8PCh. 5.4 - Prob. 9PCh. 5.4 - Prob. 10PCh. 5.4 - Prob. 11PCh. 5.4 - Prob. 12PCh. 5.4 - Prob. 13PCh. 5.4 - Prob. 14PCh. 5.4 - Interlacing of zeros. Using (21) and Rolle’s...Ch. 5.4 - Prob. 16PCh. 5.4 - Bessel’s equation. Show that for (1) the...Ch. 5.4 - Elementary Bessel functions. Derive (22) in...Ch. 5.4 - Prob. 19PCh. 5.4 - Prob. 20PCh. 5.4 - Use the powerful formulas (21) to do Probs. 19–25....Ch. 5.4 - Prob. 22PCh. 5.4 - Use the powerful formulas (21) to do Probs. 19–25....Ch. 5.4 - Use the powerful formulas (21) to do Probs. 19–25....Ch. 5.4 - Use the powerful formulas (21) to do Probs. 19–25....Ch. 5.5 - Prob. 1PCh. 5.5 - Prob. 2PCh. 5.5 - Prob. 3PCh. 5.5 - Prob. 4PCh. 5.5 - Prob. 5PCh. 5.5 - Prob. 6PCh. 5.5 - Prob. 7PCh. 5.5 - Prob. 8PCh. 5.5 - Prob. 9PCh. 5.5 - Hankel functions. Show that the Hankel functions...Ch. 5.5 - Modified Bessel functions of the first kind of...Ch. 5.5 - Prob. 13PCh. 5.5 - Reality of Iv. Show that Iv(x) is real for all...Ch. 5.5 - Modified Bessel functions of the third kind...Ch. 5 - Prob. 1RQCh. 5 - What is the difference between the two methods in...Ch. 5 - Prob. 3RQCh. 5 - Prob. 4RQCh. 5 - Write down the most important ODEs in this chapter...Ch. 5 - Can a power series solution reduce to a...Ch. 5 - What is the hypergeometric equation? Where does...Ch. 5 - List some properties of the Legendre polynomials.
Ch. 5 - Prob. 9RQCh. 5 - Can a Bessel function reduce to an elementary...Ch. 5 - POWER SERIES METHOD OR FROBENIUS METHOD
Find a...Ch. 5 - POWER SERIES METHOD OR FROBENIUS METHOD
Find a...Ch. 5 - POWER SERIES METHOD OR FROBENIUS METHOD
Find a...Ch. 5 - Prob. 14RQCh. 5 - Prob. 15RQCh. 5 - Prob. 16RQCh. 5 - Prob. 17RQCh. 5 - Prob. 18RQCh. 5 - Prob. 19RQCh. 5 - Prob. 20RQ
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