Complex variables math 5351 crn 25746, math 4370 crn 29267 spring 2021 online instructor: In function theory we work primarily with the euclidean metric, whereas in the study of functions of two real variables it is often more advantageous to use the maximum metric. In chapter ii i do the basics of.
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1) measure theory and integration, and 2) hilbert space theory, especially the spectral theorem and its applications. While there are many sides to complex analysis, or to function theory as it is known to some, it is the geometric perspective on the s bject that. The topics treated in the course include applications of the theory of residues, rouche's theorem, the argument principle, mappings by elementary functions, conformal.
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Watson, a course of modern analysis (4th ed.), camb. Press 1927 (reprinted in 1992). This course covers a number of standard classical topics from. In addition to material on the gamma function and the riemann zeta function, the text has a detailed study of elliptic functions and bessel functions, and also material on.
The course itself consists of two parts: Main source of material for the lectures:
