From Calculus to Analysis

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)