This is the fourth edition of Serge Langs <strong>Complex Analysis</strong>. The first part ofthe book covers the basic material of complex analysis and the sec... » 

This is the fourth edition of Serge Langs Complex Analysis. The first part ofthe book covers the basic material of complex analysis and the second coversmany special topics such as the Riemann Mapping Theorem the gamma functionand analytic continuation. Power series methods are used more systematicallythan in other texts and the proofs using these methods often shed more lighton the results than the standard proofs do. The first part of Complex Analysisis suitable for an introductory course on the undergraduate level and theadditional topics covered in the second part give the instructor of a graduatecourse a great deal of flexibility in structuring a more advanced course. Thisis a revised edition new examples and exercises have been added and manyminor improvements have been made throughout the text. TOCI Basic TheoryComplex Numbers and Functions. Power Series. Cauchys Theorem First Part.Winding Numbers and Cauchys Theorem. Applications of Cauchys IntegralFormula. Calculus of Residues. Conformal Mappings. Harmonic Functions. IIGeometric Function Theory Schwarz Reflection. The Riemann Mapping Theorem.Analytic Continuation Along Curves. III Various Analytic Topics Applicationsof the Maximum Modulus Principle and Jensens Formula. Entire and MeromorphicFunctions. Elliptic Functions. The Gamma and Zeta Functions. The Prime NumberTheorem. «