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Viser: Differential Geometry of Curves and Surfaces
Differential Geometry of Curves and Surfaces Vital Source e-bog
Detaljer Om Varen
- Vital Source leje e-bog 180 dage
- Udgiver: Springer Nature (September 2016)
- ISBN: 9783319397993R180
Online udgaven er tilgængelig: 180 dage fra købsdato.
Offline udgaven er tilgængelig: 180 dage fra købsdato.
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Detaljer Om Varen
- 1. Udgave
- Hardback: 320 sider
- Udgiver: Springer (September 2016)
- ISBN: 9783319397986
Over 300 color illustrations bring the mathematics to life, instantly clarifying concepts in ways that grayscale could not. Green-boxed definitions and purple-boxed theorems help to visually organize the mathematical content. Color is even used within the text to highlight logical relationships.
Applications abound! The study of conformal and equiareal functions is grounded in its application to cartography. Evolutes, involutes and cycloids are introduced through Christiaan Huygens' fascinating story: in attempting to solve the famous longitude problem with a mathematically-improved pendulum clock, he invented mathematics that would later be applied to optics and gears. Clairaut's Theorem is presented as a conservation law for angular momentum. Green's Theorem makes possible a drafting tool called a planimeter. Foucault's Pendulum helps one visualize a parallel vector field along a latitude of the earth. Even better, a south-pointing chariot helps one visualize a parallel vector field along any curve in any surface.
In truth, the most profound application of differential geometry is to modern physics, which is beyond the scope of this book. The GPS in any car wouldn't work without general relativity, formalized through the language of differential geometry. Throughout this book, applications, metaphors and visualizations are tools that motivate and clarify the rigorous mathematical content, but never replace it.
- Curves. - Additional topics in curves. - Surfaces. - The curvature of a surface. - Geodesics. - The Gauss-Bonnet theorem. -
Appendix A: The topology of subsets of R n - Recommended excursions. -