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 intended to form a bridge between calculus and analysis. It is based on the authors lecture notes used and revised nearly every year over the last decade. The book contains numerous illustrations and cross references throughout, as well as exercises with solutions at the end of each section.
Author(s): Steen Pedersen (auth.)
Edition: 1
Publisher: Springer International Publishing
Year: 2015
Language: English
Pages: 342
Tags: Integral Equations; Algebra; Analysis
Front Matter....Pages i-xix
Front Matter....Pages 1-2
Limits....Pages 3-43
Introduction to Continuity....Pages 45-50
Sets of Real Numbers....Pages 51-68
Counting....Pages 69-75
Continuity....Pages 77-89
Derivatives and Their Applications....Pages 91-126
The Riemann Integral....Pages 127-155
The Logarithm and the Exponential Function....Pages 157-173
Front Matter....Pages 174-175
Convergence of Sequences....Pages 177-204
Series....Pages 205-228
Trigonometric Functions and Applications....Pages 229-245
Fourier Series....Pages 247-279
Topology....Pages 281-295
Back Matter....Pages 297-342
