calculus on manifolds

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• Calculus on Manifolds (book) — Michael Spivak s Calculus on Manifolds: A Modern Approach to Classical Theorems of Advanced Calculus (1965, ISBN 0 8053 9021 9) is a short text treating analysis in several variables in Euclidean spaces and on differentiable manifolds. The… …   Wikipedia

• Secondary calculus and cohomological physics — In mathematics, secondary calculus is a proposed expansion of classical differential calculus on manifolds, to the space of solutions of a (nonlinear) partial differential equation. It is a sophisticated theory at the level of jet spaces and… …   Wikipedia

• Stochastic calculus — is a branch of mathematics that operates on stochastic processes. It allows a consistent theory of integration to be defined for integrals of stochastic processes with respect to stochastic processes. It is used to model systems that behave… …   Wikipedia

• Vector calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

• Classification of manifolds — In mathematics, specifically geometry and topology, the classification of manifolds is a basic question, about which much is known, and many open questions remain. Contents 1 Main themes 1.1 Overview 1.2 Different categories and additional… …   Wikipedia

• Kirby calculus — In mathematics, the Kirby calculus in geometric topology is a method for modifying framed links in the 3 sphere using a finite set of moves, the Kirby moves. It is named for Robion Kirby. Using four dimensional Cerf theory, he proved that if M… …   Wikipedia

• Multivariable calculus — Topics in Calculus Fundamental theorem Limits of functions Continuity Mean value theorem Differential calculus  Derivative Change of variables Implicit differentiation Taylor s theorem Related rates …   Wikipedia

• Differential calculus over commutative algebras — In mathematics the differential calculus over commutative algebras is a part of commutative algebra based on the observation that most concepts known from classical differential calculus can be formulated in purely algebraic terms. Instances of… …   Wikipedia

• Differential (calculus) — In mathematics, and more specifically, in differential calculus, the term differential has several interrelated meanings.Basic notions* In traditional approaches to calculus, the differential (e.g. dx, dy, dt, etc...) of a function represents an… …   Wikipedia

• Differentiable manifold — A nondifferentiable atlas of charts for the globe. The results of calculus may not be compatible between charts if the atlas is not differentiable. In the middle chart the Tropic of Cancer is a smooth curve, whereas in the first it has a sharp… …   Wikipedia

• Manifold — For other uses, see Manifold (disambiguation). The sphere (surface of a ball) is a two dimensional manifold since it can be represented by a collection of two dimensional maps. In mathematics (specifically in differential geometry and topology),… …   Wikipedia