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His text Vector Calculus(co-authored with Jerry Marsden) has been in print in six editions and five languages for 43 years Tromba's research deals with the applications of global nonlinear analysis to partial differential equations, with Morse theory for problems in the calculus of variations, and with questions concerning the properties of ...
Vector calculus or vector analysis is a branch of mathematics concerned with the differentiation and integration of vector fields, primarily in three-dimensional Euclidean space, . [1] The term vector calculus is sometimes used as a synonym for the broader subject of multivariable calculus, which spans vector calculus as well as partial differentiation and multiple integration.
Download as PDF; Printable version; ... V → W be a linear map between vector spaces V and W ... Abraham, Ralph; Marsden, Jerrold E. (1978).
Jerrold Eldon Marsden (August 17, 1942 – September 21, 2010) was a Canadian mathematician. He was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology . [ 1 ]
Vector algebra relations — regarding operations on individual vectors such as dot product, cross product, etc. Vector calculus identities — regarding operations on vector fields such as divergence, gradient, curl, etc.
The dotted vector, in this case B, is differentiated, while the (undotted) A is held constant. The utility of the Feynman subscript notation lies in its use in the derivation of vector and tensor derivative identities, as in the following example which uses the algebraic identity C⋅(A×B) = (C×A)⋅B:
In vector calculus and differential geometry the generalized Stokes theorem (sometimes with apostrophe as Stokes' theorem or Stokes's theorem), also called the Stokes–Cartan theorem, [1] is a statement about the integration of differential forms on manifolds, which both simplifies and generalizes several theorems from vector calculus.
In vector calculus, Green's theorem relates a line integral around a simple closed curve C to a double integral over the plane region D (surface in ) bounded by C. It is the two-dimensional special case of Stokes' theorem (surface in ). In one dimension, it is equivalent to the fundamental theorem of calculus.