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- https://math.libretexts.org/Courses/Misericordia_University/MTH_226%3A_Calculus_III/Chapter_16%3A_Vector_Fields%2C_Line_Integrals%2C_and_Vector_Theorems/5.11%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q4/03%3A_Vector_Calculus/3.09%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
- https://math.libretexts.org/Courses/Monroe_Community_College/MTH_212_Calculus_III/Chapter_15%3A_Vector_Fields_Line_Integrals_and_Vector_Theorems/15.8%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
- https://math.libretexts.org/Bookshelves/Calculus/Calculus_by_David_Guichard_(Improved)/16%3A_Vector_Calculus/16.09%3A_The_Divergence_TheoremThe third version of Green's Theorem can be coverted into another equation: the Divergence Theorem. This theorem related, under suitable conditions, the integral of a vector function in a region of th...The third version of Green's Theorem can be coverted into another equation: the Divergence Theorem. This theorem related, under suitable conditions, the integral of a vector function in a region of three dimensional space and to an integral over is its boundary surface.
- https://math.libretexts.org/Courses/Mission_College/Math_4A%3A_Multivariable_Calculus_(Kravets)/05%3A_Vector_Calculus/5.09%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
- https://math.libretexts.org/Under_Construction/Purgatory/MAT-004A_-_Multivariable_Calculus_(Reed)/05%3A_Vector_Calculus/5.09%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
- https://math.libretexts.org/Bookshelves/Calculus/Vector_Calculus_(Corral)/04%3A_Line_and_Surface_Integrals/4.04%3A_Surface_Integrals_and_the_Divergence_TheoremWe will now learn how to perform integration over a surface in \(\mathbb{R}^3\) , such as a sphere or a paraboloid. Recall from Section 1.8 how we identified points \((x, y, z)\) on a curve \(C\) in \...We will now learn how to perform integration over a surface in \(\mathbb{R}^3\) , such as a sphere or a paraboloid. Recall from Section 1.8 how we identified points \((x, y, z)\) on a curve \(C\) in \(\mathbb{R}^3\) , parametrized by \(x = x(t), y = y(t), z = z(t), a ≤ t ≤ b\), with the terminal points of the position vector.
- https://math.libretexts.org/Courses/Al_Akhawayn_University/MTH2301_Multivariable_Calculus/15%3A_Vector_Fields_Line_Integrals_and_Vector_Theorems/15.08%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
- https://math.libretexts.org/Courses/SUNY_Geneseo/Math_223_Calculus_3/05%3A_Vector_Calculus/5.08%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
- https://math.libretexts.org/Courses/De_Anza_College/Calculus_IV%3A_Multivariable_Calculus/03%3A_Vector_Calculus/3.09%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
- https://math.libretexts.org/Courses/Coastline_College/Math_C280%3A_Calculus_III_(Everett)/05%3A_Vector_Fields_Line_Integrals_and_Vector_Theorems/5.09%3A_The_Divergence_TheoremWe 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 “derivative” of that entity on the o...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 “derivative” 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.
