Several Real Variables
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โขThe p-norms on vector space and their equivalence
โขThe Weierstrass and Stone-Weierstrass approximation theorems
โขThe differential as a linear functional; Jacobians, Hessians, and Taylor's theorem in several variables
โขThe Implicit Function Theorem for a system of equations, proved via Banachโs Fixed Point Theorem
โขApplications to Ordinary Differential Equations
โขLine 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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The author is an expert in Spectral Theory and semigroups of operators, researching in this area for 50 years, publishing numerous papers and three monographs.
