List Of Multivariable Calculus Topics

	List Of Multivariable Calculus Topics This is a list of multivariable calculus topics. See also multivariable calculus, vector calculus, list of real analysis topics, list of calculus topics. Closed and exact differential forms Contact (mathematics) Contour integral Contour line Critical point (mathematics) Curl (mathematics) Current (mathematics) Curvature Curvilinear coordinates Del Differential form Differential operator Directional derivative Divergence Divergence theorem Double integral Equipotential surface Euler's theorem on homogeneous functions Exterior derivative Flux Frenet–Serret formulas Gauss's law Gradient Green's theorem Green's identities Harmonic function Helmholtz decomposition Hessian matrix Hodge star operator Inverse function theorem Irrotational vector field Isoperimetry Jacobian matrix Lagrange multiplier Lamellar vector field Laplacian Laplacian vector field Level set Line integral Matrix calculus * Mixed derivatives Monkey saddle Multiple integral N ... [...More Info...] [...Related Items...] OR:* [Wikipedia] [Google] [Baidu]
picture info	Multivariable Calculus 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. Multivariable calculus may be thought of as an elementary part of advanced calculus. For advanced calculus, see calculus on Euclidean space. The special case of calculus in three dimensional space is often called vector calculus. Typical operations Limits and continuity 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. :f(x,y) = \frac approaches zero whenever the point (0,0) is approached along lines through the origin (y=kx). However, when the origin is appr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
picture info	Divergence Theorem In vector calculus, the divergence theorem, also known as Gauss's theorem or Ostrogradsky's theorem, reprinted in is a theorem which relates the ''flux'' of a vector field through a closed surface to the ''divergence'' of the field in the volume enclosed. More precisely, the divergence theorem states that the surface integral of a vector field over a closed surface, which is called the "flux" through the surface, is equal to the volume integral of the divergence over the region inside the surface. Intuitively, it states that "the sum of all sources of the field in a region (with sinks regarded as negative sources) gives the net flux out of the region". The divergence theorem is an important result for the mathematics of physics and engineering, particularly in electrostatics and fluid dynamics. In these fields, it is usually applied in three dimensions. However, it generalizes to any number of dimensions. In one dimension, it is equivalent to integration by parts. In two di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]