Schaum's Outline of Differential Geometry (Schaum's)
By Martin Lipschutz
* Publisher: McGraw-Hill
* Number Of Pages: 288
* Publication Date: 1969-06-01
* ISBN-10 / ASIN: 0070379858
* ISBN-13 / EAN: 9780070379855
Product Description:
Students will find all the information covered in the standard textbooks--and more--explained clearly and concisely in this powerful study tool. Unusually detailed, it elucidates all the most difficult-to-grasp concepts that class studies and texts sometimes gloss over. The hundreds of problems with fully explained solutions illuminate important points and teach students sound problem-solving skills. Ideal, also, for independent study.
Summary: A practical elementary introduction to classical differential geometry
Rating: 5
After so many years, this book continues to be a valuable introduction to the differential geometry (DG) of curves and surfaces in euclidean 3 dimensional space, quite clear and efficient for self study, since it combines theory and problems. It reviews the necessary calculus needed. Then it goes into curves and the Frenet equations (little attention is given to plane curves) and continues with surfaces. There one finds an excellent introductory exposition of curvature and assymptotic lines, (including Meusnier, Euler, Rodrigues and Beltrami-Enneper theorems) as well as geodesic curvature, geodesics and Gauss curvature. No mention of parallel transport though (this you can find in Stoker Differential Geometry (Wiley Classics Library), in Goetz Introduction to Differential Geometry (Addison-Wesley Series in Mathematics), Millman-Parker Elements of Differential Geometry's, do Carmo Differential Geometry of Curves and Surfaces or Klingenberg's A Course in Differential Geometry (Graduate Texts in Mathematics), all of them introductory books on DG too. No global properties of curves are given, but we find a clean proof of Liebmann's theorem characterising compact connected surfaces of constant curvature as spheres (without assuming its orientabilty) and a rather sketchy proof of Gauss-Bonnet theorem. Many proofs of theoretical properties appear as problems. Practical questions are easy or not too hard to solve. If you really don't know the subject, this is a perfect start, alone or combined with those previously cited works or with Struik's classicalLectures on Classical Differential Geometry: Second Edition, or Oprea Curves and Surfaces (Graduate Studies in Mathematics) (Applied DG) or Montiel-Ros' recent book Differential Geometry and its Applications (Classroom Resource Materials) (Mathematical Association of America Textbooks). Other problem books on DG are rare. I will mention Fedenko's (Mir-Moscow) (similar to M. Lipschutz's) and Mishchenko-Solovyev-Fomenko (Problems in DG and Topology, Mir- Moscow).
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