Real Mathematical Analysis

• Main Author: Pugh, Charles C. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Edition: 2nd ed. 2015.
• Series: Undergraduate Texts in Mathematics,
• Subjects: Mathematics.; Measure theory.; Functions of real variables.; Sequences (Mathematics).; Measure and Integration.; Real Functions.; Sequences, Series, Summability.

Based on an honors course taught by the author at UC Berkeley, this introduction to undergraduate real analysis gives a different emphasis by stressing the importance of pictures and hard problems. Topics include: a natural construction of the real numbers, four-dimensional visualization, basic poin...

Table of Contents:

• Real Numbers
• A Taste of Topology
• Functions of a Real Variable
• Function Spaces
• Multivariable Calculus
• Lebesgue Theory.