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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 several variables, rather than just one. A study of limits and continuity in multivariable calculus yields many counterintuitive results not demonstrated by single-variable functions. For example, there are scalar functions of two variables with points in their domain which give different limits when approached along different paths. E.g., the function. The partial derivative generalizes the notion of the derivative to higher dimensions. A partial derivative of a multivariable function is a derivative with respect to one variable with all other variables held constant. Partial derivatives may be combined in interesting ways to create more complicated expressions of the derivative. In vector calculus, the del operator is used to define the concepts of gradient, divergence, and curl in terms of partial derivatives. A matrix of partial derivatives, the Jacobian matrix, may be used to represent the derivative of a function between two spaces of arbitrary dimension. The derivative can thus be understood as a linear transformation which directly varies from point to point in the domain of the function. Differential equations containing partial derivatives are called partial differential equations or PDEs. These equations are generally more difficult to solve than ordinary differential equations, which contain derivatives with respect to only one variable.

INTO JAPANESE

多変数微積分（多変量微積分とも呼ばれます）は、1つの変数の微積分を、複数の変数の関数を持つ微積分に拡張したものです。1つだけではなく、複数の変数を含む関数の微分と統合です。多変数微積分の限界と連続性の研究は、多くの直感に反する結果をもたらします

BACK INTO ENGLISH

Multivariable calculus (also known as multivariable calculus) is an extension of a single variable calculus to a calculus that has a function of multiple variables. Differentiation and integration of functions that contain multiple variables, not just one. Studies of the limits and continuity of multivariable calculus have had many counterintuitive results.

INTO JAPANESE

多変数微積分（多変数微積分とも呼ばれます）は、単一の変数微積分を、複数の変数の機能を持つ微積分に拡張したものです。 1つだけではなく、複数の変数を含む関数の差別化と統合。多変数微積分の限界と連続性の研究には、多くの直感に反するものがありました

BACK INTO ENGLISH

Multivariable calculus (also known as multivariable calculus) is an extension of a single variable calculus to a calculus that has the functionality of multiple variables. Differentiation and integration of functions that contain multiple variables, not just one. There are many counterintuitive studies on the limits and continuity of multivariable calculus.

INTO JAPANESE

多変数微積分（多変数微積分とも呼ばれます）は、単一の変数微積分を、複数の変数の機能を持つ微積分に拡張したものです。 1つだけではなく、複数の変数を含む関数の差別化と統合。多変数の限界と連続性に関する多くの直感に反する研究があります

BACK INTO ENGLISH

Multivariable calculus (also known as multivariable calculus) is an extension of a single variable calculus to a calculus that has the functionality of multiple variables. Differentiation and integration of functions that contain multiple variables, not just one. There are many counterintuitive studies on the limits and continuity of multivariables

INTO JAPANESE

多変数微積分（多変数微積分とも呼ばれます）は、単一の変数微積分を、複数の変数の機能を持つ微積分に拡張したものです。 1つだけではなく、複数の変数を含む関数の差別化と統合。多変数の限界と連続性に関する多くの直感に反する研究があります

BACK INTO ENGLISH

Multivariable calculus (also known as multivariable calculus) is an extension of a single variable calculus to a calculus that has the functionality of multiple variables. Differentiation and integration of functions that contain multiple variables, not just one. There are many counterintuitive studies on the limits and continuity of multivariables