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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

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"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

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

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