Elementary Differential Geometry 1st Edition by Christian Bär (PDF)

Description

The link between the physical world and its visualization is geometry. This easy-to-read, generously illustrated textbook presents an elementary introduction to differential geometry with emphasis on geometric results. Avoiding formalism as much as possible, the author harnesses basic mathematical skills in analysis and linear algebra to solve interesting geometric problems, which prepare students for more advanced study in mathematics and other scientific fields such as physics and computer science. The wide range of topics includes curve theory, a detailed study of surfaces, curvature, variation of area and minimal surfaces, geodesics, spherical and hyperbolic geometry, the divergence theorem, triangulations, and the Gauss–Bonnet theorem. The section on cartography demonstrates the concrete importance of elementary differential geometry in applications. Clearly developed arguments and proofs, colour illustrations, and over 100 exercises and solutions make this book ideal for courses and self-study. The only prerequisites are one year of undergraduate calculus and linear algebra.

User’s Reviews

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

⭐I have been rushing through books in `spare time’. This is one of them.This book is written clearly. There are some beautiful coloured graphics in the middle of the book. I would have preferred more worked examples and more illustrative graphics to amplify the text. In particular, covariant differentiation and differentiable vector fields and the stepwise approach to proof of the Gauss Bonnet theorem (i.e. triangulations).These comments almost certainly reflect my struggles with these concepts. There are answers to exercises at the back of the book and a useful bibliography.

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