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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... mathematics is the constantly increasing interrelation- ship between its various branches . Thus the present - day students of mathematics are faced with an immense mountain of material . In addition to the traditional areas of mathe ...
... mathematics is the constantly increasing interrelation- ship between its various branches . Thus the present - day students of mathematics are faced with an immense mountain of material . In addition to the traditional areas of mathe ...
vi ページ
... mathematics , and that they will be sufficiently informal that the personal tastes and attitudes of the leaders in modern mathematics will shine through clearly to the readers . The area of differential geometry is one in which recent ...
... mathematics , and that they will be sufficiently informal that the personal tastes and attitudes of the leaders in modern mathematics will shine through clearly to the readers . The area of differential geometry is one in which recent ...
viii ページ
... mathematics that Stokes ' Theorem may be con- sidered a case study in the value of generalization . In this book there are three forms of Stokes ' Theorem . The version known to Stokes appears in the last section , along with its ...
... mathematics that Stokes ' Theorem may be con- sidered a case study in the value of generalization . In this book there are three forms of Stokes ' Theorem . The version known to Stokes appears in the last section , along with its ...
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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