Essential Real Analysis

Michael Field has held appointments in the UK (Warwick University and Imperial College London), Australia (Sydney University) and the US (the University of Houston and Rice University) and has taught a wide range of courses at undergraduate and graduate level, including real analysis, partial differential equations, dynamical systems, differential manifolds, Lie groups, complex manifolds and sheaf cohomology. His publications in the areas of equivariant dynamical systems and network dynamics include nine books and research monographs as well as many research articles. His computer graphic art work, based on symmetric dynamics, has been widely exhibited and is on display at a number of universities around the world.

“This is a well written text on Real Analysis that may be used for a course in Advanced Calculus. It can also serve as a reference for advanced topics in Real Analysis.” (Charles Traina, MAA Reviews, January 4, 2020)“This book contains a reasonably complete exposition of real analysis which is needed for beginning undergraduate-level students. … This is a well-written textbook with an abundance of worked examples and exercises that are intended for a first course in analysis. This book offers a sound grounding in analysis. In particular, it gives a solid base in real analysis from which progress to more advanced topics may be made.” (Teodora-Liliana Rădulescu, zbMATH 1379.26001, 2018)

• 1 Sets, functions and the real numbers.- 2 Basic properties of real numbers, sequences and continuous functions.- 3 Infinite series.- 4 Uniform convergence.- 5 Functions.- 6. Topics from classical analysis: The Gamma-function and the Euler–Maclaurin formula.- 7 Metric spaces.- 8 Fractals and iterated function systems.- 9 Differential calculus on Rm.- Bibliography. Index.