Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced CalculusAvalon Publishing, 1965 - 144 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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... the disk cosine , jo normal hrough any el " ds of surface of the intern elds a in the secd member is perfound over a Kartin Calculus on Manifolds MATHEMATICS MONOGRAPH SERIES EDITORS : Robert Gunning. Nestminster equations of ope Front ...
... the disk cosine , jo normal hrough any el " ds of surface of the intern elds a in the secd member is perfound over a Kartin Calculus on Manifolds MATHEMATICS MONOGRAPH SERIES EDITORS : Robert Gunning. Nestminster equations of ope Front ...
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... Spivak Brandeis University Calculus on Manifolds A MODERN APPROACH TO CLASSICAL THEOREMS OF ADVANCED CALCULUS The Advanced Book Program PERSEUS BOOKS Cambridge , Massachusetts Calculus on Manifolds A Modern Approach to Classical Theorems ...
... Spivak Brandeis University Calculus on Manifolds A MODERN APPROACH TO CLASSICAL THEOREMS OF ADVANCED CALCULUS The Advanced Book Program PERSEUS BOOKS Cambridge , Massachusetts Calculus on Manifolds A Modern Approach to Classical Theorems ...
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A Modern Approach to Classical Theorems of Advanced Calculus Michael Spivak. Calculus on Manifolds A Modern Approach to Classical Theorems of Advanced Calculus Copyright © 1965 by Perseus Books Publishing , L. L. C. All rights reserved ...
A Modern Approach to Classical Theorems of Advanced Calculus Michael Spivak. Calculus on Manifolds A Modern Approach to Classical Theorems of Advanced Calculus Copyright © 1965 by Perseus Books Publishing , L. L. C. All rights reserved ...
目次
Functions on Euclidean Space | 1 |
Differentiation | 15 |
Integration | 46 |
Integration on Chains | 75 |
Integration on Manifolds | 109 |
139 | |
141 | |
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多く使われている語句
b₁ 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 Euclidean Space f(a¹ f(x¹ Figure finite number Fubini's theorem function f ƒ and g ƒ is differentiable ƒ is integrable graph of ƒ Hint inner product interior Jordan-measurable k-dimensional manifold k-form k-tensor 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 dxk Σ Σ әм მე