








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






Organization:  University of Turin 
Organization:  Politecnico di Turin 






Publisher:  Chapman & Hall/CRC (Boca Raton, FL) 
Additional cataloguing information:  ISBN13: 9780584884484 Studies in Advanced Mathematics series, Vol. 47 
  






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 GaussBonnet 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.












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, PetersonMainardiCodazzi equations, Hilberts lemma, Liebmanns theorem, canal surfaces, cyclides of Dupin, Tchebyshef patches, SineGordon equation, Bianchi transform, Kuens surface, Backlund transform, Weierstrass representation, Bjorlings formula, COstas minimal surface, Liouvilles theorem, GaussBonnet theorem












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