Complex Analysis Lecture Notes - UC Davis

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Complex Analysis Lecture NotesDan created these Notes for the courseMath 205A: Complex AnalysisItaught at UC Davis in 2016 and 2018. With a few exceptions, the expositionfollows the textbookComplex Analysisby E. M. Stein and R. Shakarchi (Prince-ton University Press, 2003). The Notes were not heavily vetted for accuracy andmay contain minor typos or errors. You can help me continue to improve themby emailing me with any comments or corrections you am grateful to Jianping Pan, Anthony Nguyen, Christo-pher Alexander, Brynn Caddel, Jennifer Brown, and Brad Velasquez for com-ments that helped me improved the Notes . Figure 5 on page 23 was created byJennifer Analysis Lecture NotesDocument version: April 20, 2018Copyrightc 2018 by Dan RomikEmail comments and feedback figure: a heat map plot of the entire functionz7 z(z 1) z/2 (z/2) (z).

p(n) ˘ 1 4 p 3n eˇ p 2n=3; where p(n) is the number ofinteger partitionsof n. •Evaluation of complicated definite integrals, for example Z 1 0 sin(t2)dt= 1 2 r ˇ 2: (This application is strongly emphasized in older textbooks, and has been known to result in a mild case of post-traumatic stress disorder.)