# Differential Geometry Of Curves And Surfaces Tapp Pdf

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- Differential Geometry of Curves and Surfaces
- Wanmin Liu
- Differential Geometry of Curves and Surfaces

*Skip to content Differential Geometry of Curves and Surfaces by Kristopher Tapp, , available at Book Depository with free delivery worldwide.*

Skip to main content Skip to table of contents. Advertisement Hide. This service is more advanced with JavaScript available. Differential Geometry of Curves and Surfaces. Front Matter Pages i-viii.

## Differential Geometry of Curves and Surfaces

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. Back in late s and early s, when I was an undergraduate, many university mathematics departments offered a course in differential geometry that focused on curves and surfaces in the plane and three-space. Things seem different now. I suspect that far fewer colleges offer courses on classical differential geometry than was the case in my day, and that many — perhaps a substantial majority — of mathematics majors graduate from college without having ever heard of things like the Frenet frame or the Gauss-Bonnet theorem.

Yet, there must still be some market for textbooks on the subject: the books by do Carmo and Struik are still in print as Dover paperbacks , and the Pearson online catalog still lists Millman and Parker as available.

In terms of topic coverage, this book follows a pretty standard path. The remaining four chapters are on surfaces. The author begins with some background multi-variable analysis the derivative of a function from one Euclidean space to another , then proceeds to a definition of a regular surface and some basic properties. The next chapter introduces the various kinds of curvature, done via a linear-algebraic look at the Gauss map, and the second fundamental form.

The final chapter states and proves the Gauss-Bonnet theorem and, in a final section, surveys some other global results, including a classification without proof of complete surfaces with constant curvature. For a first pass through the subject, I think this is a good decision — especially if, like Tapp, you are consciously trying to emphasize the geometric content of the subject.

Several things, actually. First, there is the physical appearance of the text. This is a visually appealing book, replete with many diagrams, lots of them in full color. I agree with the author that the use of color significantly helps to visualize things and assists in understanding the underlying mathematical ideas.

Color is also used to block off, in boxes, definitions and statements of theorems. I must confess to a certain cognitive dissonance here: the use of colored boxes in this way may have pedagogical benefits, but I do think that upper-level students should be taught to read mathematics without these trappings of more elementary texts.

Tapp is the author of several other books, including the very nice Matrix Groups for Undergraduates and the much more elementary Symmetry ; he knows how to write in a way that students can understand. Differential geometry can be a very thorny subject, filled with cumbersome notation and technical ideas, but the author has strived, and to the extent possible succeeded, in making these ideas intuitively plausible to the student while still writing a book that is intellectually honest and rigorous.

Third, the author has attempted to keep things down to earth by mentioning concrete applications. These applications complement but do not overwhelm the development of the mathematical theory. Finally, the selection of exercises is excellent.

There are quite a few of them, both computational and proof-oriented, and they span a broad range of difficulty. No solutions are provided in the text and there is, to my knowledge, no solutions manual for instructors. My considerable enthusiasm for this book notwithstanding, I did find a few relatively minor nits to pick. For one thing, the bibliography is inadequate. There is, for example, no listing of other books on differential geometry at or near the level of this text.

Additionally, I think that some discussion even a heuristic, expository one of the abstract idea of a manifold would have been useful. One of the values, for math majors, of studying classical differential geometry is to provide motivation for these more modern ideas.

It would have been nice for a student finishing this book to have some idea of how the notion of a surface can be generalized.

Notwithstanding these concerns, 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.

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## Wanmin Liu

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## Differential Geometry of Curves and Surfaces

It seems that you're in Germany. We have a dedicated site for Germany. 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.

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Matrix groups touch an enormous spectrum of the mathematical arena. This textbook brings them into the undergraduate curriculum. It makes an excellent one-semester course for students familiar with linear and abstract algebra and prepares them for This textbook is perfect for a math course for non-math majors, with the goal of encouraging effective analytical thinking and exposing students to elegant mathematical ideas. It includes many topics commonly found in sampler courses, like Platoni

The Basic Library List Committee suggests that undergraduate mathematics libraries consider this book for acquisition. Back in late s and early s, when I was an undergraduate, many university mathematics departments offered a course in differential geometry that focused on curves and surfaces in the plane and three-space. Things seem different now. I suspect that far fewer colleges offer courses on classical differential geometry than was the case in my day, and that many — perhaps a substantial majority — of mathematics majors graduate from college without having ever heard of things like the Frenet frame or the Gauss-Bonnet theorem. Yet, there must still be some market for textbooks on the subject: the books by do Carmo and Struik are still in print as Dover paperbacks , and the Pearson online catalog still lists Millman and Parker as available.

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Differential geometry of Curves and surfaces is a book written by Surfaces. Tapp, Kristopher. Pages The Curvature of a Surface.

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Differential Geometry of Curves and Surfaces. Kristopher Tapp. 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.

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Presenting theory while using Mathematica in a complementary way, Modern Differential Geometry of Curves and Surfaces wi Load more similar PDF files. PDF.

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Front Matter Pages i-viii PDF · Curves Kristopher Tapp Pages · Additional Topics in Curves Kristopher Tapp Pages · Surfaces Kristopher Tapp.