English | 2022 | ISBN: N/A | ASIN: B0B2MPK5PT | 293 pages | PDF | 3.08 Mb
Complex Analysis in Advanced Mathematics
In this course book, the students will learn about series of functions and power series. The concept of the radius of convergence will be introduced and calculated. This coursebook gives insight into complex integration which is different from the integration of real-valued functions. In particular, the Cauchy integral formula will be proved.
The students will learn that if a function is once (complex) differentiable then it is infinitely many times differentiable. This will be a sharp contrast with the theorems of real analysis. The various properties of MЁobius transformations have a wide variety of applications along with major theorems of theoretical interest like Cauchy-Goursat theorem, Morera's theorem,
Rouchґe's theorem and Casorati-Weierstrass theorem will be studied.
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