From Calculus to Analysis

Steen Pedersen (Autor)

Buch | Softcover

XIX, 342 Seiten

2016 | 1. Softcover reprint of the original 1st ed. 2015
Springer International Publishing (Verlag)
978-3-319-38136-7 (ISBN)

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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.

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.

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.

"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 Radulescu, zbMATH 1315.26001, 2015)

Erscheinungsdatum	14.10.2016
Zusatzinfo	XIX, 342 p. 48 illus., 14 illus. in color.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
Schlagworte	Algebra • Analysis • Calculus and mathematical analysis • Derivatives • Fourier series • Integral calculus and equations • Integral equations • Mathematics • mathematics and statistics • Number Theory • Real Variables • set theory
ISBN-10	3-319-38136-9 / 3319381369
ISBN-13	978-3-319-38136-7 / 9783319381367
Zustand	Neuware