Title
Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics),New
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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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- Q: What is the main focus of 'Differential Geometry of Curves and Surfaces'? A: The book primarily focuses on the principles of differential geometry, particularly as they apply to curves and surfaces, providing a comprehensive introduction suited for undergraduate courses.
- Q: What type of illustrations are included in the textbook? A: The textbook includes over 300 color illustrations that clarify mathematical concepts, making the material more engaging and easier to understand.
- Q: Is this book suitable for beginners in mathematics? A: Yes, this book is designed to be accessible for beginners, with minimal prerequisites and plenty of examples to aid understanding.
- Q: Who is the author of this textbook? A: The author of 'Differential Geometry of Curves and Surfaces' is Kristopher Tapp.
- Q: What edition of the book is available? A: The book is available in its first edition, published on September 27, 2016.
- Q: How many pages does the textbook have? A: The textbook contains a total of 374 pages.
- Q: What is the binding type of the book? A: The book is bound in hardcover, providing durability for regular use.
- Q: Does the book cover applications of differential geometry? A: Yes, the book discusses various applications of differential geometry, including its relevance to physics and real-world scenarios like GPS technology.
- Q: What are some key topics covered in the book? A: Key topics include conformal and equiareal functions, evolutes, involutes, cycloids, and significant theorems like Clairaut’s Theorem and Green’s Theorem.
- Q: Is this textbook suitable for advanced studies in mathematics? A: While the book is primarily aimed at undergraduates, it also serves as a solid foundation for those planning to pursue graduate studies in mathematics or physics.