Mathematical analysis : functions of several real variables and applications / Nicola Fusco, Paolo Marcellini, Carlo Sbordone ; translated by Simon G. Chiossi.
2022
QA300 .F87 2022
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Title
Mathematical analysis : functions of several real variables and applications / Nicola Fusco, Paolo Marcellini, Carlo Sbordone ; translated by Simon G. Chiossi.
Author
Fusco, Nicola, 1956- author.
Uniform Title
Analisi matematica. English
ISBN
9783031041518 electronic book
3031041518 electronic book
9783031041501
303104150X
3031041518 electronic book
9783031041501
303104150X
Published
Cham : Springer, 2022.
Language
English
Description
1 online resource (1 volume) : illustrations (black and white, and colour).
Other Standard Identifiers
10.1007/978-3-031-04151-8 doi
Call Number
QA300 .F87 2022
Dewey Decimal Classification
519.5/35
Summary
This work is a textbook on Mathematical Analysis written by expert lecturers in the field. This textbook, other than the classical differentiation and integration tools for functions of several real variables, metric spaces, ordinary differential equations, implicit function and so on, also provides opportunities to go deeper into certain topics: among them, the Ascoli-Arzela theorem, the regularity of convex functions in R^n, L^p spaces and absolutely continuous functions, all topics that are paramount in modern Mathematical Analysis. Other instances include the Weierstrass theorem on polynomial approximation of continuous functions or Peano's existence theorem (typically only existence, without uniqueness) for nonlinear ODEs and systems under general assumptions. The content is discussed in an elementary way and, at a successive stage, some topics are examined from several, more penetrating, angles. The agile organization of the subject matter helps instructors to effortlessly determine which parts to present during lectures and where to stop. The authors believe that any textbook can contribute to the success of a lecture course only to a point, and the choices made by lecturers are decisive in this respect. The book is addressed to graduate or undergraduate honors students in Mathematics, Physics, Astronomy, Computer Science, Statistics and Probability, attending Mathematical Analysis courses at the Faculties of Science, Engineering, Economics and Architecture.
Note
Includes index.
Translated from the Italian.
Translated from the Italian.
Access Note
Access limited to authorized users.
Source of Description
Description based on print version record.
Series
Unitext. Matematica per il 3+2 ; v. 137.
Available in Other Form
Mathematical analysis.
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Table of Contents
1 Sequences and Series of Functions
2 Metric Spaces and Banach Spaces
3 Functions of Several Variables
4 Ordinary Differential Equations
5 Linear Differential Equations
6 Curves and Integrals Along Curves
7 Differential One-Forms
8 Multiple Integrals
9 The Lebesgue Integral
10 Surfaces and Surface Integrals
11 Implicit Functions
12 Manifold in Rn and k-Forms.
2 Metric Spaces and Banach Spaces
3 Functions of Several Variables
4 Ordinary Differential Equations
5 Linear Differential Equations
6 Curves and Integrals Along Curves
7 Differential One-Forms
8 Multiple Integrals
9 The Lebesgue Integral
10 Surfaces and Surface Integrals
11 Implicit Functions
12 Manifold in Rn and k-Forms.