Differential Geometry of Curves and Surfaces / Undergraduate Texts in Mathematics (PDF)
(Sprache: Englisch)
This is a textbook on differential geometry well-suited 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...
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This is a textbook on differential geometry well-suited 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.
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 mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut's Theorem is presented as a conservation law for angular momentum. Green's Theorem makes possible a drafting tool called a planimeter. Foucault's Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface.
Autoren-Porträt von Kristopher Tapp
Kristopher Tapp is Professor of Mathematics at Saint Joseph's University. He has been awarded two National Science Foundation research grants to support research in differential geometry, and several teaching awards. He is the author of Symmetry: A Mathematical Exploration (Springer, 2012) and over twenty research papers featured in top journals.
Bibliographische Angaben
- Autor: Kristopher Tapp
- 2016, 1st ed. 2016, 366 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 3319397990
- ISBN-13: 9783319397993
- Erscheinungsdatum: 30.09.2016
Abhängig von Bildschirmgrösse und eingestellter Schriftgrösse kann die Seitenzahl auf Ihrem Lesegerät variieren.
eBook Informationen
- Dateiformat: PDF
- Grösse: 13 MB
- Ohne Kopierschutz
- Vorlesefunktion
Sprache:
Englisch
Pressezitat
“This is the first textbook on mathematics that I see printed in color. … This book is not a usual textbook, but a very well written introduction to differential geometry, and the colors really help the reader in understanding the figures and navigating through the text. … this book will surely serve very well for students who want to learn differential geometry from the ground up no matter what their main learning goal is.” (Árpád Kurusa, Acta Scientiarum Mathematicarum, Vol. 84 (1-2), 2018)
“This book is perfect for undergraduate students. ... There is also plenty of figures, examples, exercises and applications which make the differential geometry of curves and surfaces so interesting and intuitive. The author uses a rich variety of colours and techniques that help to clarify difficult abstract concepts.” (Teresa Arias-Marco, zbMATH 1375.53001, 2018)“This is a visually appealing book, replete with many diagrams, lots of them in full color. … the author’s writing style is extremely clear and well-motivated. … this is still the book I would use as a text for a beginning course on this subject. It would not surprise me if it quickly becomes the market leader.” (Mark Hunacek, MAA Reviews, July, 2017)
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