reader reviews of Vector Calculus, Linear Algebra, and Differential FormsVector calculus , or vector analysis , is a branch of mathematics concerned with differentiation and integration of vector fields , primarily in 3-dimensional Euclidean space R 3. Vector calculus plays an important role in differential geometry and in the study of partial differential equations. It is used extensively in physics and engineering , especially in the description of electromagnetic fields , gravitational fields and fluid flow. Vector calculus was developed from quaternion analysis by J. Willard Gibbs and Oliver Heaviside near the end of the 19th century, and most of the notation and terminology was established by Gibbs and Edwin Bidwell Wilson in their book, Vector Analysis. In the conventional form using cross products , vector calculus does not generalize to higher dimensions, while the alternative approach of geometric algebra , which uses exterior products does generalize, as discussed below.
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It seems that you're in Germany. We have a dedicated site for Germany. Classical vector analysis deals with vector fields; the gradient, divergence, and curl operators; line, surface, and volume integrals; and the integral theorems of Gauss, Stokes, and Green. Modern vector analysis distills these into the Cartan calculus and a general form of Stokes' theorem. This essentially modern text carefully develops vector analysis on manifolds and reinterprets it from the classical viewpoint and with the classical notation for three-dimensional Euclidean space, then goes on to introduce de Rham cohomology and Hodge theory. The material is accessible to an undergraduate student with calculus, linear algebra, and some topology as prerequisites. The many figures, exercises with detailed hints, and tests with answers make this book particularly suitable for anyone studying the subject independently.
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This wikibook introduces three-dimensional vectors as mathematical entities, though their application will be found, very likely, in physical science., The standard college calculus textbooks popular examples are Anton, Larson, and Stewart, although Simmons seems to be a superior text to me are supposed to provide thorough calculus training for large bodies of students with diverse background and intentions. They also form an indispensible resource for the instructor by supplying a large collection of problems for practice.