Essential Real Analysis

• Main Author: Field, Michael (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2017.
• Series: Springer Undergraduate Mathematics Series,
• Subjects: Mathematics.; Fourier analysis.; Functions of real variables.; Sequences (Mathematics).; Topology.; Real Functions.; Sequences, Series, Summability.; Fourier Analysis.

This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely f...

Table of Contents:

• 1 Sets, functions and the real numbers
• 2 Basic properties of real numbers, sequences and continuous functions
• 3 Infinite series
• 4 Uniform convergence
• 5 Functions
• 6. Topics from classical analysis: The Gamma-function and the Euler–Maclaurin formula
• 7 Metric spaces
• 8 Fractals and iterated function systems
• 9 Differential calculus on Rm
• Bibliography. Index.