This is the second textbook you can download, containing examples from the Theory of Complex Functions.

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About the author

*Leif Mejlbro* was educated as a mathematician at the *University of Copenhagen*, where he wrote his thesis on *Linear Partial Differential Operators and Distributions*. Shortly after he obtained a position at the *Technical University of Denmark*, where he remained until h...

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Description

Content

This is the second textbook you can download, containing examples from the Theory of Complex Functions. There will also be examples of complex functions, complex limits and complex line *integrals*.

This book requires knowledge of Calculus 1 and Calculus 2.

This is the second book containing examples from the *Theory of Complex Functions*. The first topic will be examples of the necessary general *topological concepts*. Then follow some examples of complex functions, complex limits and complex line *integrals*. Finally, we reach the subject itself, namely the analytic functions in general. The more specific properties of these *analytic functions* will be given in the books to follow.

Even if I have tried to be careful about this text, it is impossible to avoid errors, in particular in the first edition. It is my hope that the reader will show some understanding of my situation.

Leif Mejlbro

30th May 2008

**Introduction**

**1. Some necessary theoretical results**

**2. Topological concepts**

**3. Complex Functions**

**4. Limits**

**5. Line integrals**

**6. Differentiable and analytic functions; Cauchy-Riemann’s equations**

**7. The polar Cauchy-Riemann’s equations**

**8. Cauchy’s Integral Theorem**

**9. Cauchy’s Integral Formula**

**10. Simple applications in Hydrodynamics**