Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics) by Kristopher Tapp (PDF)

Description

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.Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed 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 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.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 wouldn’t 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.

User’s Reviews

Editorial Reviews: Review “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) From the Back Cover 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.Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed 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 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.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 wouldn’t 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. About the Author 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. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐I reviewed several books, including the usual classics such as DoCarmo, O’Neill, and Pressley, when I was designing my differential geometry course back in 2017. Then I came across this brand new book and I was just blown away by how clear, inviting, and pleasant the book is to read. The colorful figures and excellent writing make this leagues above the other standard undergrad texts and while this book does not cover the same breadth that those books do, Tapp covers the topic in such a way as to invite students to consider going further into the topic who might not otherwise. I can’t imagine ever using a different text, at least not anytime soon!

⭐A joy to read.Part of a new generation of math books that realizes rigor should be joined with illustration and explication so that the math can be readily understood. Excellent for solo self-study, class, or as a supplement to a less modern text.The illustrations are incredibly helpful and allow the reader to confirm that they’ve interpreted the formal math correctly. The occasional use of color in presenting equations also helps dramatically in quickly and efficiently parsing them. A tenet of good design and presentation that math has been slow to adopt.Let us hope for many more books from this author. I’ll be sure to buy and read any that even approach the level of quality of this one.

⭐I think this is a modern and refreshing approach to write a textbook, writing with students/learners in mind rather than showing your colleagues that your proofs are complete and the you left nothing out. Intuition first. This is one of the few books that is smooth and “inviting” to read. I hope the author keeps writing.

⭐Using this product in connection with my job

⭐Kindle’s formatting of the textbook frequently cuts important sections in half, splitting them across pages. This is especially annoying with definitions. The copy from springer.com does not seem to have this issue, although I have not read through it all yet.

⭐a very mind-opening book, excellent for math lover.

⭐Excellent

⭐Tapp’s beautiful new textbook takes advanced undergraduate writing to a whole new level. At first glance, it is visually stunning with professional formatting features and color graphics on every page. The images are more than just eye candy — many are very novel visualizations of key concepts, tremendously helpful to the reader’s understanding.Tapp’s book covers the field rigorously and concisely in only 350 pages, but manages to also include motivation and intuition for each new concept. The writing style is engaging, clear and insightful. Tapp has done a masterful job at presenting the classical mathematics both efficiently and with enough detail and examples to make the subject intelligible. There are hundreds of exercises, ranging from routine calculations to advanced excursions.The introduction says that “Applications abound!” In fact Tapp’s book does exhibit a good number of interesting connections between the mathematics and the real world (more to ground and clarify the math concepts then to apply them). I particularly like the discussion of south-pointing chariots, used to anchor the reader’s understanding of holonomy and arclength variation.I am familiar with several undergraduate differential geometry books. Do Carmo’s classic from the 1970s deserves a lot of credit. It originally served as both a textbook and a comprehensive overview of the literature. As such, Do Carmo’s exposition is sometimes cluttered with technical and peripheral topics (that Tapp wisely delegates to the exercises), and Do Carmo introduces most sections by discussing the historical context (whereas Tapp discusses the correct intuition for the upcoming mathematical content). While Carmo’s book works well for math majors at the very top universities who are bound for graduate school, it is too dry and technical for readers who require a bit more motivation to understand why each next topic is worthy of their attention.Although other authors have tried, Tapp is the first to successfully improve on Do Carmo without sacrificing its main strength, namely its sound concise rigorous mathematical development. In fact, Tapp improves even on this strength via dozens of clever proof-simplifications and organizational tricks. Tapp’s book follows the spirit of Do Carmo but is much more readable.Tapp has finally written a “curves and surfaces” book that does justice to the technical details while maintaining focused on the larger visual ideas … a book that includes the necessary local coordinate formulas without making them main point. This is an exceptionally strong manuscript that I believe deserves to become the standard undergraduate textbook in the field!

⭐In the tradition of eminent classics such by Struik (1950/1961), Kreyszig (1959), Lipschutz (1969) and Pressley (2006/2010), Tapp’s 2016 worthwhile book further notably eases the tasks of readers earnestly attempting to come to terms with differential geometry’s intricate subject matter. Visually complementing succinctly expressed algebraic statements and imparting refreshing vibrancy to the book’s many illustrations, colour graphics strengthen all important intuitive grasping of complex issues.Excellent layout and coloured headings of sections, theorems, propositions, definitions and examples also make for easier reading. Particularly interesting are the frequent exercises. Exercise 1.5 for example (If all three component functions of a space curve are quadratic functions, prove that its image is contained in a plane.), is solved by simple differentiation whereby the curve’s tangent components will be linear functions of the independent variable. The intriguing ‘tractrix’ (Klipschorn speaker) exercise 1.4 however, requires the reader to establish that d(ln(tan(t/2)))/dt=1/sin(t). In itself not really difficult of course. Nevertheless, should the author sometime get round to web-posting at least selected solutions of the book’s many stimulating exercises, many readers might well approve. In summary: a must have modern addition to differential geometry literature.

⭐What an amazing book. It’s precise and clear every step of the way.Not only is the content accurately presented but the book is incredibly aesthetic.It’s full of pictures and images, for every definition and almost every proof.It’s so full of color. It’s as good as Do Carmo’s but modern and, in my opinion, better.

⭐I didn’t use it that much because it was not a good match for the course I was doing. However the text is well written.

Keywords

Free Download Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics) in PDF format
Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics) PDF Free Download
Download Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics) 2016 PDF Free
Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics) 2016 PDF Free Download
Download Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics) PDF
Free Download Ebook Differential Geometry of Curves and Surfaces (Undergraduate Texts in Mathematics)