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Modern Differential Geometry of Curves and Surfaces with Mathematica, Third Edition

Alfred Gray
Elsa Abbena
Organization: University of Turin
Simon Salamon
Organization: Politecnico di Turin
Book information

Publisher: Chapman & Hall/CRC (Boca Raton, FL)
Copyright year: 2006
ISBN: 1584884487
Medium: Hardcover
Pages: 1016
Out of print?: N
Additional cataloguing information: ISBN-13: 9780584884484
Studies in Advanced Mathematics series, Vol. 47
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Curves in the Plane | Famous Plane Curves | Alternative Ways of Plotting Curves | New Curves from Old | Determining a Plane Curve from Its Curvature | Global Properties of Plane Curves | Curves in Space | Construction of Space Curves | Calculus on Euclidean Space | Surfaces in Euclidean Space | Nonorientable Surfaces | Metrics on Surfaces | Shape and Curvature | Ruled Surfaces | Surfaces of Revolution and Constant Curvature | A Selection of Minimal Surfaces | Intrinsic Surface Geometry | Asymptotic Curves and Geodesics on Surfaces | Principal Curves and Umbilic Points | Canal Surfaces and Cyclides of Dupin | The Theory of Surfaces of Constant Negative Curvature | Minimal Surfaces via Complex Variables | Rotation and Animation Using Quaternions | Differentiable Manifolds | Riemannian Manifolds | Abstract Surfaces and Their Geodesics | The Gauss-Bonnet Theorem

This textbook explains the classical theory of curves and surfaces, how to define and compute standard geometric functions, and how to apply techniques from analysis. With over 300 illustrations, 300 miniprograms, and many examples, it highlights important theorems and alleviates the drudgery of computations such as the curvature and torsion of a curve in space.

The third edition maintains its intuitive approach, reorganizes the material for a clearer division between the text and the Mathematica code, adds a Mathematica notebook (available online) as an appendix to each chapter, and addresses new topics such as quaternions.

*Mathematics > Calculus and Analysis > Differential Geometry

Euclidian space, semicubical parabola, regularity, cycloids, lemniscates of Bernoulli, cardioids, catenary, cissoid of diocles, tractrix, clothoids, pursuit curves, folium of Descartes, cassinian ovals, evolutes, involutes, osculating circles, pedal curves, isometries, assigned curvature, total signed curvature, trochoid curves, four vertex theorem, Reuleaux polygons, support function, fundamental theorem of space curves, loxodromes, orientability, shape operator, Gaussian curvature, helicoids, minimal surfaces, Theorema Egregium, Christoffel symbols, geodesic torsion, Frenet formulas, Clairaut patches, Peterson-Mainardi-Codazzi equations, Hilberts lemma, Liebmanns theorem, canal surfaces, cyclides of Dupin, Tchebyshef patches, Sine-Gordon equation, Bianchi transform, Kuens surface, Backlund transform, Weierstrass representation, Bjorlings formula, COstas minimal surface, Liouvilles theorem, Gauss-Bonnet theorem
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