Several Real Variables

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis
Cover of the book Several Real Variables by Shmuel Kantorovitz, Springer International Publishing
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Author: Shmuel Kantorovitz ISBN: 9783319279565
Publisher: Springer International Publishing Publication: February 9, 2016
Imprint: Springer Language: English
Author: Shmuel Kantorovitz
ISBN: 9783319279565
Publisher: Springer International Publishing
Publication: February 9, 2016
Imprint: Springer
Language: English

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:

•The p-norms on vector space and their equivalence

•The Weierstrass and Stone-Weierstrass approximation theorems

•The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables

•The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem

•Applications to Ordinary Differential Equations

•Line 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.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

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:

•The p-norms on vector space and their equivalence

•The Weierstrass and Stone-Weierstrass approximation theorems

•The differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables

•The Implicit Function Theorem for a system of equations, proved via Banach’s Fixed Point Theorem

•Applications to Ordinary Differential Equations

•Line 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.

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