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- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/03%3A_Surface_Integrals/3.03%3A_Surface_IntegralsWe are now going to define two types of integrals over surfaces.
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/06%3A_Appendices/6.01%3A_A_Appendices/6.1.06%3A_A.6_3d_Coordinate_Systems\[\begin{align*} \rho&=\text{ distance from }(0,0,0)\text{ to }(x,y,z)\\ \varphi&=\text{ angle between the $z$ axis and the line joining $(x,y,z)$ to $(0,0,0)$}\\ \theta&=\text{ angle between the $x$ ...ρ= distance from (0,0,0) to (x,y,z)φ= angle between the z axis and the line joining (x,y,z) to (0,0,0)θ= angle between the x axis and the line joining (x,y,0) to (0,0,0)
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/01%3A_Curves/1.10%3A_Optional__Planetary_MotionWe now return to the claim, made in §1.9 on central forces, that if \vecsr(t) obeys Newton's inverse square law
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/05%3A_True_False_and_Other_Short_Questions
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/00%3A_Front_Matter/02%3A_InfoPageThe LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the Californ...The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot.
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/02%3A_Vector_Fields/2.01%3A_Definitions_and_First_ExamplesIn the last chapter, we studied vector valued functions of a single variable, like, for example, the velocity of a particle at time t. Suppose however that we are interested in a fluid. There is a, ...In the last chapter, we studied vector valued functions of a single variable, like, for example, the velocity of a particle at time t. Suppose however that we are interested in a fluid. There is a, possibly different, velocity at each point in the fluid. So the velocity of a fluid is really a vector valued function of several variables. Such a function is called a vector field.
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/02%3A_Vector_Fields/2.04%3A_Line_IntegralsWe have already seen one type of integral along curves. We are now going to see a second, that turns out to have significant connections to conservative vector fields. It arose from the concept of “wo...We have already seen one type of integral along curves. We are now going to see a second, that turns out to have significant connections to conservative vector fields. It arose from the concept of “work” in classical mechanics.
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/02%3A_Vector_FieldsThumbnail: A unit sphere with surface vectors ( CC BY-SA 3.0 Unported; Cronholm144 via Wikipedia)
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/04%3A_Integral_Theorems/4.02%3A_The_Divergence_TheoremThe rest of this chapter concerns three theorems: the divergence theorem, Green's theorem and Stokes' theorem. Superficially, they look quite different from each other. But, in fact, they are all very...The rest of this chapter concerns three theorems: the divergence theorem, Green's theorem and Stokes' theorem. Superficially, they look quite different from each other. But, in fact, they are all very closely related and all three are generalizations of the fundamental theorem of calculus
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/03%3A_Surface_Integrals/3.05%3A_Orientation_of_SurfacesOne thing that made the flux integrals of the last section possible is that we could choose sensible unit normal vectors ˆn. In this section, we explain this more carefully.
- https://math.libretexts.org/Bookshelves/Calculus/CLP-4_Vector_Calculus_(Feldman_Rechnitzer_and_Yeager)/04%3A_Integral_Theorems/4.07%3A_Optional__A_Generalized_Stokes'_TheoremAs we have seen, the fundamental theorem of calculus, the divergence theorem, Greens' theorem and Stokes' theorem share a number of common features. There is in fact a single framework which encompass...As we have seen, the fundamental theorem of calculus, the divergence theorem, Greens' theorem and Stokes' theorem share a number of common features. There is in fact a single framework which encompasses and generalizes all of them, and there is a single theorem of which they are all special cases.
