Foundations of Mathematical Analysis

• Main Author: Ponnusamy, S. (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Boston, MA : Birkhäuser Boston : Imprint: Birkhäuser, 2012.
• Edition: 1.
• Subjects: Mathematics.; Mathematical analysis.; Analysis (Mathematics).; Approximation theory.; Fourier analysis.; Applied mathematics.; Engineering mathematics.; Analysis.; Applications of Mathematics.; Approximations and Expansions.; Fourier Analysis.

Mathematical analysis is fundamental to the undergraduate curriculum not only because it is the stepping stone for the study of advanced analysis, but also because of its applications to other branches of mathematics, physics, and engineering at both the undergraduate and graduate levels. This self-...

Table of Contents:

• Real Number System
• Sequences: Convergence and Divergence
• Limits, Continuity, and Differentiability
• Applications of Differentiability
• Series: Convergence and Divergence
• Definite and Indefinite Integrals
• Improper Integrals and Applications of Riemann Integrals
• Power Series
• Uniform Convergence of Sequences of Functions
• Fourier Series and Applications
• Functions of Bounded Variation and Riemann-Stieltjes Integrals
• References
• Index of Special Notations
• Hints for Selected Questions and Exercises
• Index.