Complex Analysis

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This wikibook shall be an introduction to complex analysis and introduce the reader to the basic constructions and techniques which are usually associated with this subject. A characteristic of this particular textbook is that it attempts to connect complex analysis to many different areas of mathematics, such as algebra, functional analysis, geometry, number theory, real analysis and topology. This shall help the reader, and in particular the reader familiar with such matters, to memorize the subject more quickly and this approach will also include tools being used in proofs which are universally applicable.

Contents[edit]

  1. Complex numbers
  2. Complex differentiability
  3. Function and power series
  4. Curve and contour integration
  5. Trigonometry
  6. Cauchy's theorem and Cauchy's integral formula
  7. The compact-open topology
  8. Local theory of holomorphic functions
  9. Integration over chains
  10. Global theory of holomorphic functions
  11. Bibliography