Title
Differential Geometry Of Curves And Surfaces (Undergraduate Texts In Mathematics),Used
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This Is A Textbook On Differential Geometry Wellsuited To A Variety Of Courses On This Topic. For Readers Seeking An Elementary Text, The Prerequisites Are Minimal And Include Plenty Of Examples And Intermediate Steps Within Proofs, While Providing An Invitation To More Excursive Applications And Advanced Topics. For Readers Bound For Graduate School In Math Or Physics, This Is A Clear, Concise, Rigorous Development Of The Topic Including The Deep Global Theorems. For The Benefit Of All Readers, The Author Employs Various Techniques To Render The Difficult Abstract Ideas Herein More Understandable And Engaging.Over 300 Color Illustrations Bring The Mathematics To Life, Instantly Clarifying Concepts In Ways That Grayscale Could Not. Greenboxed Definitions And Purpleboxed Theorems Help To Visually Organize The Mathematical Content. Color Is Even Used Within The Text To Highlight Logical Relationships.Applications Abound! The Study Of Conformal And Equiareal Functions Is Grounded In Its Application To Cartography. Evolutes, Involutes And Cycloids Are Introduced Through Christiaan Huygens' Fascinating Story: In Attempting To Solve The Famous Longitude Problem With A Mathematicallyimproved Pendulum Clock, He Invented Mathematics That Would Later Be Applied To Optics And Gears. Clairauts Theorem Is Presented As A Conservation Law For Angular Momentum. Greens Theorem Makes Possible A Drafting Tool Called A Planimeter. Foucaults Pendulum Helps One Visualize A Parallel Vector Field Along A Latitude Of The Earth. Even Better, A Southpointing Chariot Helps One Visualize A Parallel Vector Field Along Any Curve In Any Surface.In Truth, The Most Profound Application Of Differential Geometry Is To Modern Physics, Which Is Beyond The Scope Of This Book. The Gps In Any Car Wouldnt Work Without General Relativity, Formalized Through The Language Of Differential Geometry. Throughout This Book,Applications, Metaphors And Visualizations Are Tools That Motivate And Clarify The Rigorous Mathematical Content, But Never Replace It.
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This product may contain chemicals known to the State of California to cause cancer, birth defects, or other reproductive harm.
For more information, please visit www.P65Warnings.ca.gov.
- Q: How many pages does this book have? A: This book has three hundred seventy-four pages. It offers a comprehensive exploration of differential geometry.
- Q: What is the binding type of this textbook? A: The binding type is hardcover. This provides durability and protection for frequent use.
- Q: What are the dimensions of this book? A: The dimensions are six point twenty-six inches in length, one inch in width, and nine point twenty-five inches in height. This size makes it portable for students.
- Q: What level of mathematics knowledge is required to read this book? A: Minimal mathematics knowledge is required. The book is suitable for both beginners and those pursuing graduate studies.
- Q: Is this book suitable for self-study? A: Yes, this book is suitable for self-study. It includes plenty of examples and detailed proofs to facilitate understanding.
- Q: Is this textbook suitable for undergraduates? A: Yes, it is designed for undergraduate students. It provides clear explanations and engaging illustrations.
- Q: How should I care for this hardcover book? A: To care for this hardcover book, keep it in a dry place and avoid exposing it to direct sunlight. This will help preserve its condition.
- Q: Can I use this book for advanced topics in differential geometry? A: Yes, it covers advanced topics as well. It serves as a bridge to more excursive applications in the field.
- Q: What should I do if my book arrives damaged? A: If your book arrives damaged, contact customer support for a replacement or refund. They will guide you through the return process.
- Q: Does this book include illustrations? A: Yes, it includes over three hundred color illustrations. These visuals enhance the understanding of complex concepts.
- Q: Is there a warranty for this textbook? A: No, there is no warranty for textbooks. However, you can return it if it arrives damaged.
- Q: Can this book help with understanding general relativity? A: Yes, it provides foundational knowledge relevant to general relativity. It discusses applications that are essential in physics.
- Q: Is this book intended for beginners in mathematics? A: Yes, it is intended for beginners. It requires minimal prerequisites and is structured to build understanding gradually.
- Q: What are the main themes covered in this book? A: The main themes include curves, surfaces, and their applications in various fields such as physics and cartography.
- Q: How can I visualize the concepts in this book? A: You can visualize concepts through its numerous illustrations and examples, which clarify abstract ideas effectively.
- Q: Is there a glossary or definition section in the book? A: Yes, the book features green-boxed definitions to help organize and clarify mathematical terms throughout the text.