Advanced Calculus: Differential Calculus and Stokes' Theorem PDF
314 Pages·2016·11.329 MB·English
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Description:
This textbook offers a high-level introduction to multi-variable differential calculus. Differential forms are introduced incrementally in the narrative, eventually leading to a unified treatment of Green’s, Stokes’ and Gauss’ theorems. Furthermore, the presentation offers a natural route to differential geometry. Contents:Calculus of Vector FunctionsTangent Spaces and 1-formsLine IntegralsDifferential Calculus of MappingsApplications of Differential CalculusDouble and Triple IntegralsWedge Products and Exterior DerivativesIntegration of FormsStokes’ Theorem and Applications Numerous figures allow for easy-to-grasp explanations of the mathematical concepts. Differential forms are used throughout the book to motivate vector calculus. Includes the necessary material from linear algebra, set theory & basic topology.
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