Search
- Filter Results
- Location
- Classification
- Include attachments
- https://math.libretexts.org/Courses/Lake_Tahoe_Community_College/Interactive_Calculus_Q4/03%3A_Vector_Calculus/3.08%3A_Stokes_TheoremIn this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalizatio...In this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalization of the Fundamental Theorem of Calculus to higher dimensions. Stokes’ theorem relates a vector surface integral over surface S in space to a line integral around the boundary of S.
- 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/SUNY_Geneseo/Math_223_Calculus_3/05%3A_Vector_Calculus/5.07%3A_Stokes_TheoremIn this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalizatio...In this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalization of the Fundamental Theorem of Calculus to higher dimensions. Stokes’ theorem relates a vector surface integral over surface S in space to a line integral around the boundary of S.
- 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/Courses/University_of_Maryland/MATH_241/05%3A_Vector_Calculus/5.08%3A_Stokes%E2%80%99_TheoremIn this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalizatio...In this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalization of the Fundamental Theorem of Calculus to higher dimensions. Stokes’ theorem relates a vector surface integral over surface S in space to a line integral around the boundary of S.
- https://math.libretexts.org/Bookshelves/Calculus/Supplemental_Modules_(Calculus)/Vector_Calculus/4%3A_Integration_in_Vector_Fields/4.z10%3A_Stokes%E2%80%99_TheoremIn this section we see the generalization of a familiar theorem, Green’s Theorem. Just as before we are interested in an equality that allows us to go between the integral on a closed curve to the dou...In this section we see the generalization of a familiar theorem, Green’s Theorem. Just as before we are interested in an equality that allows us to go between the integral on a closed curve to the double integral of a surface. Some important definitions to know before proceeding are: simple closed curve, divergence, flux, curl, and normal vector. Knowing how to calculate the determinant of 2x2 and 3x3 matrices will also help deepen your understanding of divergence and curl.
- 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/Mission_College/Math_4A%3A_Multivariable_Calculus_v2_(Reed)/16%3A_Vector_Calculus/16.07%3A_Stokes_TheoremIn this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalizatio...In this section, we study Stokes’ theorem, a higher-dimensional generalization of Green’s theorem. This theorem, like the Fundamental Theorem for Line Integrals and Green’s theorem, is a generalization of the Fundamental Theorem of Calculus to higher dimensions. Stokes’ theorem relates a vector surface integral over surface S in space to a line integral around the boundary of S.
- https://math.libretexts.org/Courses/Misericordia_University/MTH_171-172%3A_Calculus_-_Early_Transcendentals_(Stewart)/16%3A_Vector_Calculus/16.08%3A_Stokes'_TheoremSo far the only types of line integrals which we have discussed are those along curves in R2 . But the definitions and properties which were covered in Sections 4.1 and 4.2 can easily be extended to i...So far the only types of line integrals which we have discussed are those along curves in R2 . But the definitions and properties which were covered in Sections 4.1 and 4.2 can easily be extended to include functions of three variables, so that we can now discuss line integrals along curves in R3 .
- https://math.libretexts.org/Courses/University_of_California_Davis/UCD_Mat_21D%3A_Vector_Analysis/Integration_in_Vector_Fields/16.7%3A_Stokes'_TheoremIn this section we see the generalization of a familiar theorem, Green’s Theorem. Just as before we are interested in an equality that allows us to go between the integral on a closed curve to the dou...In this section we see the generalization of a familiar theorem, Green’s Theorem. Just as before we are interested in an equality that allows us to go between the integral on a closed curve to the double integral of a surface. Some important definitions to know before proceeding are: simple closed curve, divergence, flux, curl, and normal vector. Knowing how to calculate the determinant of 2x2 and 3x3 matrices will also help deepen your understanding of divergence and curl.
