Analysis II

Buch | Softcover
XII, 400 Seiten
2008 | 2008
Springer Basel (Verlag)
978-3-7643-7472-3 (ISBN)

Lese- und Medienproben

Analysis II - Herbert Amann, Joachim Escher
85,59 inkl. MwSt
The second volume of this introduction into analysis deals with the integration theory of functions of one variable, the multidimensional differential calculus and the theory of curves and line integrals. It continues the modern and clear development that started in Volume I.

As with the first, the second volume contains substantially more material than can 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 find 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 colleagues 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 final version. We also extend great thanks to our staff 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 effort 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 Birkhauser 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.

Erscheint lt. Verlag 16.5.2008
Zusatzinfo XII, 400 p.
Verlagsort Cham
Sprache englisch
Maße 170 x 244 mm
Gewicht 692 g
Themenwelt Mathematik / Informatik Mathematik Analysis
Schlagworte Analysis • Calculation • Calculus • Complex Analysis • Derivation • Derivative • differential equation • Equation • Fourier series • Function • gamma function • Hardcover, Softcover / Mathematik/Analysis • HC/Mathematik/Analysis • manifold • Meromorphic Function • Real analysis • Variable
ISBN-10 3-7643-7472-1 / 3764374721
ISBN-13 978-3-7643-7472-3 / 9783764374723
Zustand Neuware
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