Congestion
发表于 2025-3-30 10:23:09
Clotting Factor Antibodies (Inhibitors),We shall now consider the local behavior of curvature on an .-surface. The way in which an .-surface curves around in ℝ.. is measured by the way the normal direction changes as we move from point to point on the surfacc. In order to measure the rate of changc of the normal direction, we need to be able to differentiate vector fields on .-surfaces.
不怕任性
发表于 2025-3-30 12:49:56
http://reply.papertrans.cn/31/3075/307430/307430_52.png
Nucleate
发表于 2025-3-30 16:56:26
https://doi.org/10.1007/978-1-4614-3752-9In this chapter we shall establish two theorems which show that, locally, .-surfaces and parametrized .-surfaces are the same. In order to do this, we will need to use the following theorem from the calculus of several variables.
卜闻
发表于 2025-3-30 23:43:50
Dale Salwak (Professor of English)We consider now the problem of how to find the volume (area when . = 2) of an .-surface in ℝ... As with the length of plane curves, this is done in two steps. First we define the volume of a parametrized .-surface and then we define the volume of an .-surface in terms of local parametrizations.
fatuity
发表于 2025-3-31 01:19:54
Haemodialysis — a personal viewpointLet ϕ: . → ℝ.. be a parametrized .-surface in ℝ... A . of ϕ is a smooth map .: . x (−ɛ, ɛ) → ℝ.. with the property that .(.,0) = ϕ(.) for all . ∈ .. Thus a variation surrounds the .-surface ϕ with a family of singular .-surfaces ϕ.: . → ℝ.. (−ɛ < ɛ < ɛ) defined by ϕ . (.) = .(., .).
Notorious
发表于 2025-3-31 06:18:00
Vector Fields,The tool which will allow us to study the geometry of level sets is the calculus of vector fields. In this chapter we develop some of the basic ideas.
nullify
发表于 2025-3-31 09:16:40
http://reply.papertrans.cn/31/3075/307430/307430_57.png
过分自信
发表于 2025-3-31 13:37:37
http://reply.papertrans.cn/31/3075/307430/307430_58.png
发展
发表于 2025-3-31 19:39:18
http://reply.papertrans.cn/31/3075/307430/307430_59.png
Relinquish
发表于 2025-4-1 00:53:49
http://reply.papertrans.cn/31/3075/307430/307430_60.png