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Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach
Using a dual presentation that is rigorous and comprehensive?yet exceptionaly reader-friendly in approach?this book covers most of the standard topics in multivariate calculus and an introduction to linear algebra. It focuses in underlying ideas, integrates theory and applications, offers a host of learning aids, features coverage of differential forms, and emphasizes numerical methods that highlight modern applications of mathematics. The revised and expanded content of this edition includes new discussions of functions; complex numbers; closure, interior, and boundary; orientation; forms restricted to vector spaces; expanded discussions of subsets and subspaces of R^n; probability, change of basis matrix; and more. For individuals interested in the fields of mathematics, engineering, and science?and looking for a unified approach and better understanding of vector calculus, linear algebra, and differential forms.
800 pages, Hardcover
First published January 1, 1998
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Displaying 1 - 4 of 4 reviews
March 7, 2012
An excellent companion to Spivak's "Calculus on Manifolds", this text engagingly bridges the gap between the Gibbs formulation of vector calculus and the modern Cartan formulation using differential forms so that one can properly study differential geometry. Gives many excellent exercises and examples of curious behavior. It is also exceptionally reader-friendly; the authors sprinkle historical anecdotes and modern applications throughout the text and have a voice that is very down-to-earth.
January 6, 2021
I read parts of the last chapter to help me with Spivak and it was really really good. It does in 150 pages what spivak does in about 40, which is mostly a testament of how terse the latter is. I expect to return to this this term for my diff geo class.
January 17, 2025
A classic for a reason. A bit difficult as an introduction to multivariate calculus and proofs though. Goes off the rails a bit when differential forms are introduced but the payoff is worth it. Once you get to generalized Stokes theorem its very satisfying in its simplicity, though its only simple because of all the knowledge you build up beforehand.
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March 15, 2020Its good for which class and is it best for 12th standard
Displaying 1 - 4 of 4 reviews