From Calculus to Analysis

• Main Author: Pedersen, Steen (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2015.
• Subjects: Mathematics.; Algebra.; Mathematical analysis.; Analysis (Mathematics).; Integral equations.; Integral Equations.; Analysis.

This textbook features applications including a proof of the Fundamental Theorem of Algebra, space filling curves, and the theory of irrational numbers.  In addition to the standard results of advanced calculus, the book  contains several interesting applications of these results. The text is intend...

Table of Contents:

• Part I
• Limits
• Introduction to Continuity
• Sets of Real Numbers
• Counting
• Continuity
• Derivatives and their Applications
• The Riemann Integral
• The Logarithm and the Exponential Function
• Part II
• Convergence of Sequences
• Series
• Trigonometric Functions and Applications
• Fourier Series
• Topology
• Appendices.