Differential Geometry of Curves and Surfaces (Revised and Updated Second Edition)
by Manfredo P. do Carmo · Dover Publications
Standard undergraduate text covering curves in three-space — arc-length parameterization, curvature, torsion, the Frenet frame — before local and global surface theory. The Dover revised edition adds corrections and updated notes; exercises range from routine to demanding. Chapter 1 is a complete treatment of curve theory (arclength, curvature, torsion, Frenet apparatus, global results).
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