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Multivariable calculus information



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]

Multivariable calculus may be thought of as an elementary part of advanced calculus. For advanced calculus, see calculus on Euclidean space. The special case of calculus in three dimensional space is often called vector calculus.

  1. ^ Richard Courant; Fritz John (14 December 1999). Introduction to Calculus and Analysis Volume II/2. Springer Science & Business Media. ISBN 978-3-540-66570-0.

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Multivariable calculus

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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:...

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List of multivariable calculus topics

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a list of multivariable calculus topics. See also multivariable calculus, vector calculus, list of real analysis topics, list of calculus topics. Closed...

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Vector calculus

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The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial...

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Matrix calculus

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In mathematics, matrix calculus is a specialized notation for doing multivariable calculus, especially over spaces of matrices. It collects the various...

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Advanced calculus

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calculus can refer to Multivariable calculus Mathematical analysis; specifically, real analysis A branch of calculus that goes beyond multivariable calculus;...

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Steinmetz solid

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In geometry, a Steinmetz solid is the solid body obtained as the intersection of two or three cylinders of equal radius at right angles. Each of the curves...

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List of calculus topics

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of infinitesimals For further developments: see list of real analysis topics, list of complex analysis topics, list of multivariable calculus topics....

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Area

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requires multivariable calculus. Area plays an important role in modern mathematics. In addition to its obvious importance in geometry and calculus, area...

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Math 55

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less than 10% were advised to enroll in a course such as Math 21: Multivariable Calculus (19 students). In the past, problem sets were expected to take from...

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Discrete mathematics

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mathematics excludes topics in "continuous mathematics" such as real numbers, calculus or Euclidean geometry. Discrete objects can often be enumerated by integers;...

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Directional derivative

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A directional derivative is a concept in multivariable calculus that measures the rate at which a function changes in a particular direction at a given...

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Second partial derivative test

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mathematics, the second partial derivative test is a method in multivariable calculus used to determine if a critical point of a function is a local minimum...

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Function of several real variables

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f(x). The calculus of such vector fields is vector calculus. For more on the treatment of row vectors and column vectors of multivariable functions,...

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Partial derivative

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Iterated integral Jacobian matrix and determinant Laplace operator Multivariable calculus Symmetry of second derivatives Triple product rule, also known as...

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Mathematical analysis

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Constructive analysis History of calculus Hypercomplex analysis Multiple rule-based problems Multivariable calculus Paraconsistent logic Smooth infinitesimal...

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Multiple integral

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In mathematics (specifically multivariable calculus), a multiple integral is a definite integral of a function of several real variables, for instance...

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Volume integral

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In mathematics (particularly multivariable calculus), a volume integral (∭) is an integral over a 3-dimensional domain; that is, it is a special case of...

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Integral

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A differential form is a mathematical concept in the fields of multivariable calculus, differential topology, and tensors. Differential forms are organized...

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Gaussian integral

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Gaussian integral can be solved analytically through the methods of multivariable calculus. That is, there is no elementary indefinite integral for ∫ e − x...

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Leibniz integral rule

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basic form of Leibniz's Integral Rule, the multivariable chain rule, and the First Fundamental Theorem of Calculus. Suppose f {\displaystyle f} is defined...

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Fundamental theorem of calculus

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Stokes' theorem (sometimes known as the fundamental theorem of multivariable calculus): Let M be an oriented piecewise smooth manifold of dimension n...

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Inverse function theorem

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gives a formula for the derivative of the inverse function. In multivariable calculus, this theorem can be generalized to any continuously differentiable...

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Outline of calculus

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Differential calculus Integral calculus Multivariable calculus Fractional calculus Differential Geometry History of calculus Important publications in calculus Continuous...

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Jacobian matrix and determinant

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In vector calculus, the Jacobian matrix (/dʒəˈkoʊbiən/, /dʒɪ-, jɪ-/) of a vector-valued function of several variables is the matrix of all its first-order...

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Calculus

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McCallum, William G.; Gleason, Andrew M.; et al. (2013). Calculus: Single and Multivariable (6th ed.). Hoboken, NJ: Wiley. ISBN 978-0-470-88861-2. OCLC 794034942...

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Surface integral

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In mathematics, particularly multivariable calculus, a surface integral is a generalization of multiple integrals to integration over surfaces. It can...

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