Several real variables [electronic resource] / Shmuel Kantorovitz.

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Several real variables [electronic resource] / Shmuel Kantorovitz.

9783319279565 (electronic book)
3319279564 (electronic book)
9783319279558

Cham : Springer, 2016.

English

1 online resource (xii, 307 pages) : illustrations.

10.1007/978-3-319-27956-5 doi

QA331.5

515/.84

This undergraduate textbook is based on lectures given by the author on the differential and integral calculus of functions of several real variables. The book has a modern approach and includes topics such as: ℓ́ØThe p-norms on vector space and their equivalence ℓ́ØThe Weierstrass and Stone-Weierstrass approximation theorems ℓ́ØThe differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables ℓ́ØThe Implicit Function Theorem for a system of equations, proved via Banachℓ́ℓs Fixed Point Theorem ℓ́ØApplications to Ordinary Differential Equations ℓ́ØLine integrals and an introduction to surface integrals This book features numerous examples, detailed proofs, as well as exercises at the end of sections. Many of the exercises have detailed solutions, making the book suitable for self-study. Several Real Variables will be useful for undergraduate students in mathematics who have completed first courses in linear algebra and analysis of one real variable.

Includes bibliographical references and index.

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Online resource; title from PDF title page (SpringerLink, viewed February 18, 2016).

Springer undergraduate mathematics series.

Print version: 9783319279558

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