Analysis II

• Κύριοι συγγραφείς: Amann, Herbert (Συγγραφέας), Escher, Joachim (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Basel : Birkhäuser Basel, 2008.
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Functional analysis.; Functions of complex variables.; Special functions.; Analysis.; Functions of a Complex Variable.; Special Functions.; Functional Analysis.; Mathematics, general.

 As with the ?rst, the secondvolume containssubstantially morematerialthancan be covered in a one-semester course. Such courses may omit many beautiful and well-grounded applications which connect broadly to many areas of mathematics. We of course hope that students will pursue this material independently; teachers may ?nd it useful for undergraduate seminars. For an overview of the material presented, consult the table of contents and the chapter introductions. As before, we stress that doing the numerous exercises is indispensable for understanding the subject matter, and they also round out and amplify the main text. In writing this volume, we are indebted to the help of many. We especially thank our friends and colleages Pavol Quittner and Gieri Simonett. They have not only meticulously reviewed the entire manuscript and assisted in weeding out errors but also, through their valuable suggestions for improvement, contributed essentially to the ?nal version. We also extend great thanks to our sta? for their careful perusal of the entire manuscript and for tracking errata and inaccuracies. Our most heartfelt thank extends again to our “typesetting perfectionist”, 1 without whose tireless e?ort this book would not look nearly so nice. We also thank Andreas for helping resolve hardware and software problems. Finally, we extend thanks to Thomas Hintermann and to Birkh¨ auser for the good working relationship and their understanding of our desired deadlines. 

 Preface -- VI. Integral Calculus in One Variable - 1. Step Continuous Functions - 2. Continuous Extensions - 3. The Cauchy-Riemann Integral - 4. Properties of the Integral - 5. The Technology of Integration - 6. Sums and Integrals - 7. Fourier Series - 8. Improper Integrals - 9. The Gamma Function -- VII. Differential Calculus in Several Variables - 1. Continuous Linear Mappings - 2. Differentiability - 3. Calculation Rules - 4. Multilinear Mappings - 5. Higher Derivatives - 6. Nemytski Operators and Calculus of Variations - 7. Inverse Mappings - 8. Implicit Functions - 9. Manifolds - 10. Tangents and Normals -- VIII. Line Integrals - 1. Curves and Their Length - 2. Curves in Rn - 3. Pfaff Forms - 4. Line Integrals - 5. Holomorphic Functions - 6. Meromorphic Functions -- Bibliography -- Index.