Overview

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 Functions Tangent Spaces and 1-forms Line Integrals Differential Calculus of Mappings Applications of Differential Calculus Double and Triple Integrals Wedge Products and Exterior Derivatives Integration of Forms Stokes’ Theorem and Applications

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9783110438215

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Reviews

The characteristic features of the book are the abundance of worked examples, illustrated by nicely drawn suggestive gures and the excellent layout [...]. There are also exercises at the end of each section. The book is clearly written, in a pleasant style, and can be recommended as a textbook for advanced calculus courses. Tiberiu Trif in: Stud. Univ. Babes-Bolyai Math. 62 (2017), 2, S. 269-271 Quibbles aside, I'm greatly impressed by this book. There is a very nice section on differential operators, and the treatment of double and triple integrals leads naturally to the idea of integration of forms and integrals on a surface. Also, by restricting discussion to one, two and three forms in a geometric context, the book avoids many of those daunting generalities on differential forms. Such features, together with an abundant provision of practice exercises (no hints or solutions) make this an ideal teaching text. MAA Reviews

The characteristic features of the book are the abundance of worked examples, illustrated by nicely drawn suggestive gures and the excellent layout [...]. There are also exercises at the end of each section. The book is clearly written, in a pleasant style, and can be recommended as a textbook for advanced calculus courses. Tiberiu Trif in: Stud. Univ. Babes-Bolyai Math. 62 (2017), 2, S. 269-271

The characteristic features of the book are the abundance of worked examples, illustrated by nicely drawn suggestive gures and the excellent layout [...]. There are also exercises at the end of each section. The book is clearly written, in a pleasant style, and can be recommended as a textbook for advanced calculus courses. Tiberiu Trif in: Stud. Univ. Babes-Bolyai Math. 62 (2017), 2, S. 269-271 Quibbles aside, I'm greatly impressed by this book. There is a very nice section on differential operators, and the treatment of double and triple integrals leads naturally to the idea of integration of forms and integrals on a surface. Also, by restricting discussion to one, two and three forms in a geometric context, the book avoids many of those daunting generalities on differential forms. Such features, together with an abundant provision of practice exercises (no hints or solutions) make this an ideal teaching text. MAA Reviews

The characteristic features of the book are the abundance of worked examples, illustrated by nicely drawn suggestive gures and the excellent layout [...]. There are also exercises at the end of each section. The book is clearly written, in a pleasant style, and can be recommended as a textbook for advanced calculus courses. Tiberiu Trif in: Stud. Univ. Babes-Bolyai Math. 62 (2017), 2, S. 269-271

Author Information

Pietro-Luciano Buono, University of Ontario Institute of Technology, Canada.

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