From Calculus to Analysis

Steen Pedersen

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English

Springer International Publishing AG
09 October 2016

Algebra; Calculus & mathematical analysis; Integral calculus & equations

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.

By: Steen Pedersen
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: Softcover reprint of the original 1st ed. 2015
Dimensions: Height: 235mm, Width: 155mm, Spine: 19mm
Weight: 5.504kg
ISBN: 9783319381367
ISBN 10: 3319381369
Pages: 342
Publication Date: 09 October 2016
Audience: Professional and scholarly , Undergraduate
Format: Paperback
Publisher's Status: Active

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.

Steen Pedersen, Ph.D. is a Professor of Mathematics at Wright State University in Dayton, Ohio, USA. His research interests include fractals, metric geometry, fourier analysis, spectral theory, and operator algebras.

Reviews for From Calculus to Analysis

“This book is mainly addressed to undergraduate students and it is intended to be a two-semester analysis course for these students. … As the title suggests, this textbook is intended to fill the gap between a calculus course and a student’s first serious real analysis course. … Undergraduates and some advanced high-school seniors will find this text a useful and pleasant experience in the classroom or as a self-study guide.” (Teodora-Liliana Rădulescu, zbMATH 1315.26001, 2015)