Twenty-One Lectures on Complex Analysis : A First Course. 1st ed. 2017

種類:

電子ブック

責任表示:

by Alexander Isaev

出版情報:

Cham : Springer International Publishing : Imprint: Springer, 2017

著者名:

• Isaev, Alexander.
• SpringerLink (Online service)

シリーズ名:

Springer Undergraduate Mathematics Series ;

ISBN:

9783319681702 [3319681702]    

注記:

1. Complex Numbers. The Fundamental Theorem of Algebra -- 2. R- and C-Differentiability -- 3 The Stereographic Projection. Conformal Maps. The Open Mapping Theorem -- 4. Conformal Maps (Continued). Möbius Transformations -- 5. Möbius Transformations (Continued). Generalised Circles. Symmetry -- 6. Domains Bounded by Pairs of Generalised Circles. Integration -- 7. Primitives Along Paths. Holomorphic Primitives on a Disk. Goursat’s Lemma -- 8. Proof of Lemma 7.2. Homotopy. The Riemann Mapping Theorem -- 9. Cauchy’s Independence of Homotopy Theorem. Jordan Domains -- 10. Cauchy’s Integral Theorem. Proof of Theorem 3.1. Cauchy’s Integral Formula -- 11. Morera’s Theorem. Power Series. Abel’s Theorem. Disk and Radius of Convergence -- 12. Power Series (Cont’d). Expansion of a Holomorphic Function. The Uniqueness Theorem -- 13. Liouville’s Theorem. Laurent Series. Isolated Singularities -- 14. Isolated Singularities (Continued). Poles and Zeroes. Isolated Singularities at infinity -- 15. Isolated Singularities at in
At its core, this concise textbook presents standard material for a first course in complex analysis at the advanced undergraduate level. This distinctive text will prove most rewarding for students who have a genuine passion for mathematics as well as certain mathematical maturity. Primarily aimed at undergraduates with working knowledge of real analysis and metric spaces, this book can also be used to instruct a graduate course. The text uses a conversational style with topics purposefully apportioned into 21 lectures, providing a suitable format for either independent study or lecture-based teaching. Instructors are invited to rearrange the order of topics according to their own vision. A clear and rigorous exposition is supported by engaging examples and exercises unique to each lecture; a large number of exercises contain useful calculation problems. Hints are given for a selection of the more difficult exercises. This text furnishes the reader with a means of learning complex analysis as well as a subtl

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