Analysis II Differential and Integral Calculus, Fourier Series, Holomorphic Functions /

• Κύριος συγγραφέας: Godement, Roger (Συγγραφέας)
• Συγγραφή απο Οργανισμό/Αρχή: SpringerLink (Online service)
• Μορφή: Ηλεκτρονική πηγή Ηλ. βιβλίο
• Γλώσσα: English
• Έκδοση: Berlin, Heidelberg : Springer Berlin Heidelberg, 2005.
• Σειρά: Universitext
• Θέματα: Mathematics.; Measure theory.; Functions of real variables.; Real Functions.; Measure and Integration.

Functions in R and C, including the theory of Fourier series, Fourier integrals and part of that of holomorphic functions, form the focal topic of these two volumes. Based on a course given by the author to large audiences at Paris VII University for many years, the exposition proceeds somewhat nonl...

Πίνακας περιεχομένων:

• Differential and Integral Calculus
• The Riemann Integral
• Integrability Conditions
• The “Fundamental Theorem” (FT)
• Integration by parts
• Taylor’s Formula
• The change of variable formula
• Generalised Riemann integrals
• Approximation Theorems
• Radon measures in ? or ?
• Schwartz distributions
• Asymptotic Analysis
• Truncated expansions
• Summation formulae
• Harmonic Analysis and Holomorphic Functions
• Analysis on the unit circle
• Elementary theorems on Fourier series
• Dirichlet’s method
• Analytic and holomorphic functions
• Harmonic functions and Fourier series
• From Fourier series to integrals.