From Calculus to Analysis

ISBN-13: 9783319381367 / Angielski / Miękka / 2016 / 342 str.

Steen Pedersen

Opis

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.

Recenzje

"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)

Spis treści

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.

O autorze

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.

Blurb

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