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Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one variable to calculus with functions of several variables: the differentiation and integration of functions involving multiple variables ( multivariate ), rather than just one. [1]
with Jerrold Marsden: Vector Calculus, Freeman, San Francisco, 5th edition 2003 (with the participation of Michael Hoffman and Joanne Seitz) with Jerrold Marsden and Alan Weinstein: Basis multivariable calculus, Freeman 2000; Theory of Branched Minimal Surfaces, Springer Verlag 2012; References
In mathematics (specifically multivariable calculus ), a multiple integral is a definite integral of a function of several real variables, for instance, f(x, y) or f(x, y, z) . Integrals of a function of two variables over a region in (the real-number plane) are called double integrals, and integrals of a function of three variables over a ...
A complex-valued function of several real variables may be defined by relaxing, in the definition of the real-valued functions, the restriction of the codomain to the real numbers, and allowing complex values. If f(x1, …, xn) is such a complex valued function, it may be decomposed as. where g and h are real-valued functions.
Calculus on Manifolds is a brief monograph on the theory of vector-valued functions of several real variables (f : R n →R m) and differentiable manifolds in Euclidean space. . In addition to extending the concepts of differentiation (including the inverse and implicit function theorems) and Riemann integration (including Fubini's theorem) to functions of several variables, the book treats ...
Exact differential. In multivariate calculus, a differential or differential form is said to be exact or perfect ( exact differential ), as contrasted with an inexact differential, if it is equal to the general differential for some differentiable function in an orthogonal coordinate system (hence is a multivariable function whose variables are ...
For functions of a single variable, the theorem states that if is a continuously differentiable function with nonzero derivative at the point ; then is injective (or bijective onto the image) in a neighborhood of , the inverse is continuously differentiable near = (), and the derivative of the inverse function at is the reciprocal of the derivative of at : ′ = ′ = ′ (()).
Books. Burke Hubbard is the author of a popular mathematics book on wavelet transforms, originally published in French as Ondes et ondelettes: la saga d’un outil mathématique (Pour la Science, 1995). It won the Prix d'Alembert [ fr] of the Société mathématique de France, [4] [6] and Hubbard became the first winner of this prize who was ...
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