Comments on Chapter 2

Page 6: In the proof of Theorem 2.1.10, it should be observed that the function \(F\) is well defined: namely, the integral is independent of the choice of polygonal path. This independence follows directly from the hypothesis that the integral of \(f\) over an arbitrary closed path is equal to zero. See Remark (c) on page 7.
Page 8: In the displayed formula at the bottom of the page, the sentence-ending period is on the wrong side of \(dz\).
Page 12: A period is missing at the end of the fourth displayed formula.
Page 13: In displayed equation (1), the differential \(dw\) is missing in the second integral.
Page 16: In the first displayed equation, the numerator of the integrand should be \(f_n(w)\), not \(f(w)\).
Page 17: In Problem 2, for \(\sum_n z^n\) read \(\sum_n a_n z^n\).
Page 18: In Problem 9 part (c), for “if \(x\) is not real” read “if \(z\) is not real”. The notation \(e^{iw}\) is a synonym for \(\exp(iw)\), as explained on page 20. At the end of the problem, insert a closing right-hand parenthesis.
Page 22: At line 3, there is an absolute-value sign missing: \(z|\to\infty\) should be \(|z|\to\infty\).; Two lines from the bottom of the page, for “out” read “our”.
Page 25: In item (d), line 1, delete the word “is”.