This book not only explains and develops the classical theory of curves, but also allows the reader to reproduce and study curves and surfaces using computer methods. This second edition contains eight new chapters on global curve theory, space curves, minimal surfaces, inversions, cyclides, the Gauss-Bonnet Theorem and global surface theory.

1.curves in the plane 2.studying curves in the plane with mathematica 3.famous plane curves 4.alternate methods for plotting plane curves 5.new curves from old 6.determining a plane curve from its curvature 7.global properties of plane curves 8.curves in space 9.tubes and knots 10.construction to space curves 11.calculus on euclidean space 12.surfaces in euclidean space 13.examples of surfaces 14.nonorientable surfaces 15.metrics on surfaces 16.surfaces in 3-dimensional space 17.surfaces in 3-dimensional space via mathematica 18.asymptotic curves on surfaces 19.ruled surfaces 20.surfaces of revolution 21.surfaces of constant gaussian curvature 22.intrinsic surface geometry 23.differentiable manifolds 24.riemannian manifolds 25.abstract surfaces 26.geodesics on sufaces 27.the gauss-bonnet theorem 28.principal curves and umbilic points 29.triply orthogonal systems of surfaces 30.minimal surfaces and complex variables 32.minimal surfaces via the weierstrass representation 33.minimal surfaces via bjorling's formula 34.construction of surfaces 35.canal surfaces and cyclides of dupin 36.inversions of curves and surfaces

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