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. |
この書籍内から
検索結果1-3 / 10
39 ページ
... result to the case of a continuously differen- tiable function f : R " → Rm with m < n . 2-38 . ( a ) If f : R → R satisfies f ' ( a ) 1-1 ( on all of R ) . 0 for all a ER , show that ƒ is ( b ) Define f : R2 R2 by f Differentiation 39.
... result to the case of a continuously differen- tiable function f : R " → Rm with m < n . 2-38 . ( a ) If f : R → R satisfies f ' ( a ) 1-1 ( on all of R ) . 0 for all a ER , show that ƒ is ( b ) Define f : R2 R2 by f Differentiation 39.
41 ページ
... satisfies The answer is provided by 2-12 Theorem ( Implicit Function Theorem ) . Suppose f : R " X Rm → Rm is continuously differentiable in an open set containing ( a , b ) and f ( a , b ) = 0. Let M be the m × m matrix ( Dn + ifi ( a ...
... satisfies The answer is provided by 2-12 Theorem ( Implicit Function Theorem ) . Suppose f : R " X Rm → Rm is continuously differentiable in an open set containing ( a , b ) and f ( a , b ) = 0. Let M be the m × m matrix ( Dn + ifi ( a ...
66 ページ
... satisfies Saf = ( -1 ) " / n and f ( x ) = 0 for x any An . Show that f ( 0.1 ) f does not exist , but lim ( e.1 - e ) f = log 2 . 3-38 . Let An be a closed set contained in ( n , n + 1 ) . Suppose that f : RR satisfies SA , f = ( - 1 ) ...
... satisfies Saf = ( -1 ) " / n and f ( x ) = 0 for x any An . Show that f ( 0.1 ) f does not exist , but lim ( e.1 - e ) f = log 2 . 3-38 . Let An be a closed set contained in ( n , n + 1 ) . Suppose that f : RR satisfies SA , f = ( - 1 ) ...
他の版 - すべて表示
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