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.
Rezensionen / Stimmen
"This textbook is excellent for self-study as it contains a lot of well-chosen examples and complete proofs. Each topic is followed by a set of suitable exercises, accompanied with detailed solutions, which complement the presented material significantly. . The reader can obtain a very deep insight into analysis and related theories as the book provides deep understanding of principles." (Roza Aceska, zbMATH 1405.26003, 2019)
Reihe
Auflage
Sprache
Verlagsort
Verlagsgruppe
Springer International Publishing
Zielgruppe
Für Beruf und Forschung
Upper undergraduate
Illustrationen
16
16 s/w Abbildungen
XII, 307 p. 16 illus.
Maße
Höhe: 235 mm
Breite: 155 mm
Dicke: 18 mm
Gewicht
ISBN-13
978-3-319-27955-8 (9783319279558)
DOI
10.1007/978-3-319-27956-5
Schweitzer Klassifikation
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.
Continuity.- Derivation.- Implicit Functions.- Integration.- Solutions.
