Differential geometry is the study of curved spaces using the techniques of calculus. It is a mainstay of undergraduate mathematics education and a cornerstone of modern geometry. It is also the language used by Einstein to express general relativity, and so is an essential tool for astronomers and theoretical physicists. This introductory textbook originates from a popular course given to third year students at Durham University for over twenty years, first by the late L. M. Woodward and later by John Bolton (and others). It provides a thorough introduction by focusing on the beginnings of the subject as studied by Gauss: curves and surfaces in Euclidean space. While the main topics are the classics of differential geometry – the definition and geometric meaning of Gaussian curvature, the Theorema Egregium, geodesics, and the Gauss–Bonnet Theorem – the treatment is modern and student-friendly, taking direct routes to explain, prove and apply the main results. It includes many exercises to test students’ understanding of the material, and ends with a supplementary chapter on minimal surfaces that could be used as an extension towards advanced courses or as a source of student projects.
Reviews (4)
4 reviews for A First Course in Differential Geometry: Surfaces in Euclidean Space
MSussman
Rated 5 out of 5
January 10, 2022
An accessible and complete book for undergraduate modeling course, lots of homework problems
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JLaPorte
Rated 5 out of 5
November 18, 2019
This book has all of the classical undergraduate problems explained well and accessible to any student. The book covers a lot of material that can be ...More
This book has all of the classical undergraduate problems explained well and accessible to any student. The book covers a lot of material that can be used as a resource in many other classes.
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LTalionis
Rated 5 out of 5
February 7, 2016
I fail to understand the poor reviews of this EXCELLENT introductory text on mathematical modelling. Practitioners of mathematics are known for their ...More
I fail to understand the poor reviews of this EXCELLENT introductory text on mathematical modelling. Practitioners of mathematics are known for their masochistic love of proofs and rigor, and when covering more advanced concepts, authors of mathematics textbooks make the mistake of assuming that their audience is versed in high-level mathematics (because who else would they be reading an advanced mathematics textbook, right?). However, I research for a living, and my job requires that I master many areas of knowledge quickly and efficiently despite the fact that my quantitative skills are not the best. Therefore, I have mastered the ability to find references that sufficiently cover advanced concepts in a seemingly oxymoronic basic and accessible manner. Such books are rare, but this is precisely what the author has done in this instance. Having reviewed many, MANY books on Mathematical modelling, the subject matter simply does not get any easier or clearer than this. In my opinion, if the reader cannot grasp the concepts laid forth so plainly in this AMAZING textbook, then they probably should not be pursuing a major that requires any mathematical modelling at all. Kudos to the author. I hope to see more good work like this in the future.
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dee
Rated 5 out of 5
September 11, 2015
great introductory book to mathematical modeling
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4 reviews for A First Course in Differential Geometry: Surfaces in Euclidean Space