Calculus On Manifolds: A Modern Approach To Classical Theorems Of Advanced CalculusAvalon Publishing, 1965 - 160 ページ This little book is especially concerned with those portions of ”advanced calculus” in which the subtlety of the concepts and methods makes rigor difficult to attain at an elementary level. The approach taken here uses elementary versions of modern methods found in sophisticated mathematics. The formal prerequisites include only a term of linear algebra, a nodding acquaintance with the notation of set theory, and a respectable first-year calculus course (one which at least mentions the least upper bound (sup) and greatest lower bound (inf) of a set of real numbers). Beyond this a certain (perhaps latent) rapport with abstract mathematics will be found almost essential. |
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viii ページ
... theorem of the book . This theorem ( Stokes ' Theorem ) has had a curious history and has undergone a striking ... Divergence Theorem . These three theorems , the classical theorems of the subtitle , are derived quite easily from a ...
... theorem of the book . This theorem ( Stokes ' Theorem ) has had a curious history and has undergone a striking ... Divergence Theorem . These three theorems , the classical theorems of the subtitle , are derived quite easily from a ...
134 ページ
... , also known as the counterclockwise orientation . ) Proof . This is a very d ( a dx + ẞ dy ) = ( D18 - special case of Theorem 5-5 , since D2α ) dx dy . Ʌ || 5-8 Theorem ( Divergence Theorem ) . Let MCR3 be 134 Calculus on Manifolds XXVI.
... , also known as the counterclockwise orientation . ) Proof . This is a very d ( a dx + ẞ dy ) = ( D18 - special case of Theorem 5-5 , since D2α ) dx dy . Ʌ || 5-8 Theorem ( Divergence Theorem ) . Let MCR3 be 134 Calculus on Manifolds XXVI.
142 ページ
... Divergence of a field , 88 , 137 Divergence Theorem , 135 Domain , 11 Element of length , 126 Element of volume , see Volume Convergence , 137 Coordinate condition , 111 Coordinate system , 111 Dual space , 5 polar , 73 Cover , 7 ...
... Divergence of a field , 88 , 137 Divergence Theorem , 135 Domain , 11 Element of length , 126 Element of volume , see Volume Convergence , 137 Coordinate condition , 111 Coordinate system , 111 Dual space , 5 polar , 73 Cover , 7 ...
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多く使われている語句
boundary bounded function calculus called closed curves closed rectangle continuously differentiable coordinate system Define f defined by f(x,y definition denoted Df(a Dif(a differentiable function div F dx¹ equation f(a¹ f(x¹ Figure finite number Fubini's theorem function f ƒ and g ƒ is differentiable ƒ is integrable Hint inner product interior Jordan-measurable k-dimensional manifold k-form k-tensor least upper bound Let A CR Let f lim h→0 linear transformation matrix Michael Spivak Möbius strip ms(f n-chain notation open cover open rectangle open set open set containing orientation-preserving partial derivatives partition of unity Problem Proof prove Show that ƒ singular n-cube Stokes subrectangle subset Suppose Theorem 2-2 unique usual orientation V₁ vector field vector space volume element Ʌ dx Ʌ dxi Σ Σ