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Lectures on Classical Differential Geometry: Second Edition (Dover Books on Mathematics)

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This book has developed from a one-term course in differential geometry given for juniors, seniors, and graduate students at the Massachusetts Institute of Technology. It presents the fundamental conceptions of the theory of curves and surfaces and applies them to a number of examples. Some care is given to historical, biographical, and bibliographical material, not only to keep alive the memory of the men to whom we owe the main structure of our present elementary differential geometry, but also to allow the student to go back to the sources, which still contain many precious ideas for further thought.

No author on this subject is without primary obligation to the two standard treatises of Darboux and Bianchi, who, around the turn of the century, collected the result of more than a century of research, themselves adding greatly to it. Other fundamental works constantly consulted by the author are Eisenhart's Treatise, Scheffers' Anwendung, and Blaschke's Vorlesungen. Years of teaching from Graustein's Differential Geometry have also left their imprint on the presentation of the material.

Excellent brief introduction presents fundamental theory of curves and surfaces and applies them to a number of examples. Topics include curves, theory of surfaces, fundamental equations, geometry on a surface, envelopes, conformal mapping, minimal surfaces, more. Well-illustrated, with abundant problems and solutions. Bibliography.

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