κ Differential Geometry

Сургамж

Calculus on curved things. Curvature measures how a surface bends, geodesics are its straight lines, and manifolds let the same ideas run in any dimension. Einstein's equations are a statement in this language.

Сургамж

Зарим хичээлүүд нь нээлттэй текстээс авсан: Wikipedia. Сургалтын хуудас бүрийн эх үүсвэр, лицензийг тодорхойлно.

Энд ашигласан тэмдэгтүүд

Бүх тодорхойлолт, зураг, үсгийн утгыг харахын тулд ямар ч тэмдэгтийг дарна уу.

f'(x)derivative
Instantaneous rate of change; slope of the graph.\frac{\partial f}{\partial x}partial derivative
Derivative with respect to x, holding the other variables fixed.\nabla fgradient (nabla, del)
Vector of partial derivatives; points uphill.\kappacurvature, Gaussian curvature
How fast a curve turns; the product of a surface's principal curvatures.

Хүмүүс асуудаг асуултууд

What is curvature?

For a curve, how fast its direction turns per unit length; for a surface, Gauss's combination of the two principal bendings, and Gauss's theorem says it can be measured from inside the surface without leaving it.

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Тоглоомын хуудаснаа бичээд эсвэл зур. Бүх алхам, зураг, хариулт нь асуулт асуух хүртэл нуугдаж байдаг. Засварлах →

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