Mathematical Analysis II

• Κύριος συγγραφέας: Zorich, Vladimir A. (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2016.
• Έκδοση: 2nd ed. 2016.
• Σειρά: Universitext,
• Θέματα: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Physics.; Analysis.; Theoretical, Mathematical and Computational Physics.

This second English edition of a very popular two-volume work presents a thorough first course in analysis, leading from real numbers to such advanced topics as differential forms on manifolds; asymptotic methods; Fourier, Laplace, and Legendre transforms; elliptic functions; and distributions. Espe...

Πίνακας περιεχομένων:

• 9 Continuous Mappings (General Theory)
• 10 Differential Calculus from a General Viewpoint
• 11 Multiple Integrals
• 12 Surfaces and Differential Forms in Rn
• 13 Line and Surface Integrals
• 14 Elements of Vector Analysis and Field Theory
• 15 Integration of Differential Forms on Manifolds
• 16 Uniform Convergence and Basic Operations of Analysis
• 17 Integrals Depending on a Parameter
• 18 Fourier Series and the Fourier Transform
• 19 Asymptotic Expansions
• Topics and Questions for Midterm Examinations
• Examination Topics
• Examination Problems (Series and Integrals Depending on a Parameter)
• Intermediate Problems (Integral Calculus of Several Variables)
• Appendices: A Series as a Tool (Introductory Lecture)
• B Change of Variables in Multiple Integrals
• C Multidimensional Geometry and Functions of a Very Large Number of Variables
• D Operators of Field Theory in Curvilinear Coordinates
• E Modern Formula of Newton–Leibniz
• References
• Index of Basic Notation
• Subject Index
• Name Index.