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Modern Differential Geometry of Curves and Surfaces with Mathematica
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:
Alfred Gray
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CRC
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2 edition
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1088 pages
ISBN
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0849371643
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450 Point
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
"I would recommend this book to anyone that needs an intuitive introduction to the subject that is complete in many ways and that provides visualization and examples using mathematica when needed. Before purchasing this I was expecting the treatment to be 'informal' and using mathematica rather than mathematical rigour to introduce concepts and results. This is not the case however. In my opinion the author has struck the right balance between a formal maths treatment and the abilities provided by mathematica to make the book easier to read and coprehend."
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