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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vi ページ
... Stokes ' Theorem , some- times called the fundamental theorem of multivariate calculus , is traditionally taught in ... Stoke's Theorem as the modern working mathematician sees it . A student with a good course in calculus and linear ...
... Stokes ' Theorem , some- times called the fundamental theorem of multivariate calculus , is traditionally taught in ... Stoke's Theorem as the modern working mathematician sees it . A student with a good course in calculus and linear ...
viii ページ
... Stokes ; by the time of his death the result was known universally as Stokes ' Theorem . At least three proofs were given by his contemporaries : Thomson published one , another appeared in Thomson and Tait's Treatise on Natural ...
... Stokes ; by the time of his death the result was known universally as Stokes ' Theorem . At least three proofs were given by his contemporaries : Thomson published one , another appeared in Thomson and Tait's Treatise on Natural ...
104 ページ
... Stokes ' theorem possible , the reader should be willing to grant the first two of these attributes to Stokes ' theorem . the book is devoted to justifying the third . The rest of Problems . 4-25 . ( Independence of parameterization ) ...
... Stokes ' theorem possible , the reader should be willing to grant the first two of these attributes to Stokes ' theorem . the book is devoted to justifying the third . The rest of Problems . 4-25 . ( Independence of parameterization ) ...
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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