{"id":113,"date":"2021-07-30T17:15:08","date_gmt":"2021-07-30T17:15:08","guid":{"rendered":"https:\/\/courses.lumenlearning.com\/calculus3\/?post_type=chapter&p=113"},"modified":"2022-11-01T05:35:19","modified_gmt":"2022-11-01T05:35:19","slug":"introduction-to-the-divergence-theorem","status":"publish","type":"chapter","link":"https:\/\/courses.lumenlearning.com\/calculus3\/chapter\/introduction-to-the-divergence-theorem\/","title":{"raw":"Introduction to the Divergence Theorem","rendered":"Introduction to the Divergence Theorem"},"content":{"raw":"

We have examined several versions of the Fundamental Theorem of Calculus in higher dimensions that relate the integral around an oriented boundary of a domain to a \u201cderivative\u201d of that entity on the oriented domain. In this section, we state the divergence theorem, which is the final theorem of this type that we will study. The divergence theorem has many uses in physics; in particular, the divergence theorem is used in the field of partial differential equations to derive equations modeling heat flow and conservation of mass. We use the theorem to calculate flux integrals and apply it to electrostatic fields.<\/p>","rendered":"

We have examined several versions of the Fundamental Theorem of Calculus in higher dimensions that relate the integral around an oriented boundary of a domain to a \u201cderivative\u201d of that entity on the oriented domain. In this section, we state the divergence theorem, which is the final theorem of this type that we will study. The divergence theorem has many uses in physics; in particular, the divergence theorem is used in the field of partial differential equations to derive equations modeling heat flow and conservation of mass. We use the theorem to calculate flux integrals and apply it to electrostatic fields.<\/p>\n\n\t\t\t

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