Abstract
We next turn to functions of a complex variable, that are perhaps best known for solving integrals by contour deformation in the complex plane.
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Notes
- 1.
Here, D is an open subset of the complex plane which is simply connected.
- 2.
A closed contour \(\gamma \) divides the complex plane into a region \(I(\gamma )\) within \(\gamma \) and an unbounded region outside, according to the Jordan curve theorem.
- 3.
Known as the Riemann-Lebesgue theorem in Fourier transforms, see e.g., van Putten, M.H.P.M., 1998, SIAM Rev., 40(2), 333.
- 4.
Giacinto Morera 1856–1909.
- 5.
More on this in Chap. 6.
- 6.
An excellent introduction to classical fluid dynamics is [1].
References
Batchelor, G.K., An Introduction to Fluid Dynamics (Cambridge University Press, Cambridge, 1990)
van Putten, M.H.P.M., PNAS, 2006, 103, 519
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van Putten, M.H. (2017). Complex Function Theory. In: Introduction to Methods of Approximation in Physics and Astronomy. Undergraduate Lecture Notes in Physics. Springer, Singapore. https://doi.org/10.1007/978-981-10-2932-5_2
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DOI: https://doi.org/10.1007/978-981-10-2932-5_2
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