A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition - Hardcover

Michael Spivak

Hardcover

ISBN 10: 0914098721 ISBN 13: 9780914098720

Publisher: Publish or Perish, 1999

Synopsis

A Comprehensive Introduction to Differential Geometry, Vol. 3, 3rd Edition by Michael Spivak is an essential resource for advanced mathematics students, researchers, and professionals. This volume delves into the intricate interplay of geometry, topology, and analysis, providing a thorough and comprehensive understanding of differential geometry. Unique features of this edition include detailed explanations and rigorous proofs that enhance the reader's understanding of complex concepts, numerous illustrations and diagrams that aid in visualizing geometric structures, and a blend of classical and modern approaches to differential geometry, making it a versatile reference for both traditional and contemporary studies. Exercises at the end of each chapter reinforce learning and encourage further exploration. This volume is part of a five-volume series that is celebrated for its depth and clarity, making it a valuable addition to any mathematician's library.

About this title

About the Author

Michael David Spivak, born on May 25, 1940, is an American mathematician with a profound impact on the field of differential geometry. As an expositor of mathematics, he has skillfully bridged the gap between complex theory and accessible explanations. Spivak’s legacy extends beyond academia—he is also the visionary behind Publish-or-Perish Press. 📚 Author of the Five-Volume Masterpiece: Spivak’s magnum opus, “A Comprehensive Introduction to Differential Geometry,” stands as a testament to his mathematical prowess. This five-volume work is a treasure trove for those seeking a deep understanding of geometric concepts. 🔍 Why Choose Spivak? 🌟 Clarity and Precision: Spivak’s writing style demystifies intricate topics, making them approachable for learners at all levels. 🌟 Problem-Solving Focus: Dive into challenging problems guided by a master mathematician. 🌟 Mathematical Rigor: Immerse yourself in proofs, theorems, and applications—the hallmark of Spivak’s approach. 📖 About the Mathematician: Hailing from Queens, New York, Spivak earned his Ph.D. from Princeton University. His contributions have left an indelible mark on mathematics, and his passion for clarity continues to inspire generations of learners. 🛒 Explore Spivak’s Work: Whether you’re a student, educator, or lifelong learner, delve into the intricacies of calculus, geometry, and mathematical reasoning with Michael Spivak. 📚🔢

Excerpt. © Reprinted by permission. All rights reserved.

Partial differential equations have played a decisive role in our investigations ever since they were first introduced in Chapter 6 of Volume I. To be sure, at times we have suppressed the equations themselves in favor of a more geometric conception involving k-dimensional distributions, and on other occasions we have instead expressed things in terms of differential forms. But, in one form or another, the Frobenius Theorem (which represents everything we know about partial differential equations) was used in discussing Lie groups, ordinary and affine theory of curves and surfaces in space (where Lie group methods were used), in all our proofs of the Test Case, in the proof of the Fundamental Theorem of Surface Theory, and in the generalizations of this theorem which were given in Chapter 7

Edition details

• Publisher: Publish or Perish
• Publication date: 1999
• ISBN 10: 0914098721
• ISBN 13: 9780914098720
• Binding: Hardcover
• Language: English
• Edition number: 3
• Number of pages: 328