Abstract
In previous chapters, we introduced complex functions and studied properties of three essential tools: derivatives, integrals, and series of complex functions. In this chapter, we derive some exciting applications of complex analysis based on one formula, known as Cauchy’s residue theorem.
After having thought about this subject, and brought together the diverse results mentioned above, I had the hope of establishing on a direct and rigorous analysis the passage from the real to the imaginary; and my research has lead me to this Memoire.
-Augustin-Louis Cauchy (1789–1857) [Writing about his Memoire of 1814, which contained the residue theorem and several computations of real integrals by complex methods.]
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Asmar, N.H., Grafakos, L. (2018). Residue Theory. In: Complex Analysis with Applications. Undergraduate Texts in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-94063-2_5
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DOI: https://doi.org/10.1007/978-3-319-94063-2_5
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-94062-5
Online ISBN: 978-3-319-94063-2
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