In this course, the student will delve deeper into the study of advanced topics in complex analysis of sequences and series, study their divergence and convergence, important theories to study their properties, and study complex integration in a detailed manner with several important theories such as Cauchy's theory of integration and Cauchy's theorem for integration - path independence theorem - loop theorem - Cauchy's formula theorem as well Taylor and Laurent theories and the use of Laurent's theory in the classification of tensile points.
Intended learning outcomes
That the student relates between real sequences and complex series in a clear way.
The student should explain the solutions in the examples, especially the convergence test, accurately.
That the student draws the areas of convergence of the series in a good and clear manner.
The student should mention several series and learn how to deduce them using some theories well.
That the student links between theories and use them to solve divergence and convergence of sequences and series in a good way.
The student should mention the complex integral, its properties and theories related to integration well.
To explain the Taylor and Laurent series accurately and clearly.