[request_ebook] Vector Calculus, Linear Algebra, and Differential Forms: A Unified Approach

Description

This text covers most of the standard topics in multivariate calculus and a substantial part of a standard first course in linear algebra. If, in addition, one teaches the proofs in Appendix A, the book can be used as a textbook for a course in analysis.The organization and selection of material differs from the standard approach in four ways.

• We integrate linear algebra and multivariate calculus.
  
• We emphasize computationally effective algorithms, and prove theorems by showing that those algorithms really work. This better reflects the way this mathematics is used today, in both applied and in pure mathematics.
  
  
• we use differential forms to generalize the fundamental theorem of calculus to higher dimensions. This gives one elegant theorem, the generalized Stokes's theorem, that works in all dimensions. In contrast, vector calculus requires special formulas, operators, and theorems for each dimension where it works.
  
  
• We provide a new approach to Lebesgue integration.

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