Differential geometry has a long, wonderful history. It has found relevance in areas ranging from machinery design to the classification of four-manifolds to the creation of theories of nature's fundamental forces to the study of DNA. This book studies the differential geometry of surfaces with the goal of helping students make the transition from the compartmentalized courses in a standard university curriculum to a type of mathematics that is a unified whole. It mixes together geometry, calculus, linear algebra, differential equations, complex variables, the calculus of variations, and notions from the sciences. Differential geometry is not just for mathematics majors. It is also for students in engineering and the sciences. The mix of ideas offer students the opportunity to visualize concepts through the use of computer algebra systems such as Maple. The book emphasizes that this visualization goes hand-in-hand with the understanding of the mathematics behind the computer construction. Students will not only see geodesics on surfaces, but they will also observe the effect that an abstract result such as the Clairaut relation can have on geodesics. Furthermore, the book shows how the equations of motion of particles constrained to surfaces are actually types of geodesics. The book is rich in results and exercises that form a continuous spectrum, from those that depend on calculation to proofs that are quite abstract.
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Elegant and digestible, even under the worst circumstances.
评分除了出错的地方以外还都挺好的，习题和定理结合的form很合我口味。我觉得可以多介绍介绍notation conventions。
评分除了出错的地方以外还都挺好的，习题和定理结合的form很合我口味。我觉得可以多介绍介绍notation conventions。
评分除了出错的地方以外还都挺好的，习题和定理结合的form很合我口味。我觉得可以多介绍介绍notation conventions。
评分很基础，详尽。喜欢用字母表示出fundamental form的每个element，基于此算出各种相关内容，如geodesic的表示，有实际应用价值，每章最后都有code可以作图。跳了minimal surface,略读了黎曼几何部分。
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