Real Analysis: Examples, Concepts, and Applications
Rudi Weikard · Steven Redolfi · Ahmed Ghatasheh
Apr. 2026 · Academic Press
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"Real Analysis: Examples, Concepts, and Applications" instructs in core proofs, theorems, and approaches of real analysis, as illustrated via compelling exercises and carefully crafted, practical examples. From chapter one onward, students are asked to apply concepts to reinforce understanding and gain applied experience in real analysis. In particular, exercises challenge students to use key proofs of major real analysis theorems to encourage independent thinking and problem solving, and new areas of research powered by real analysis are introduced. Following early chapters on core concepts and approaches of real analysis, the authors apply real analysis across integration on product spaces, radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among other topics. Advanced exercises are also included at the end of each chapter, with exercise difficulty level noted for instructors, and solutions included in an appendix.• Applies real analysis-based problem solving across a range of mathematical topics, from product spaces to radon functionals, bounded variation and lebesgue-stieltjes measures, convolutions, probability, and differential equations, among others• Reinforces understanding of core concepts, proofs, and theorems of real analysis to encourage independent thinking• Features additional exercises at the end of each chapter and solutions in an appendix
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Rudi Weikard is Professor of Mathematics at the University of Alabama at Birmingham who has frequently taught the Real Analysis sequence. He has authored or co-authored over 60 scholarly articles, co-edited three volumes of conference proceedings, and recently a co-authored (with C. Bennewitz and B.M. Brown) a textbook on Spectral and Scattering Theory for Ordinary Differential Equations.Steven Redolfi graduated with a PhD in Applied Mathematics from the University of Alabama at Birmingham and is currently a Model Validation Analyst for Regions Financial Corporation. He has coauthored papers and given talks on topics which heavily rely on the general integration theory introduced in Real Analysis.Ahmed Ghatasheh graduated with a PhD in Applied Mathematics from the University of Alabama at Birmingham (UAB). After graduation, he taught at The Ohio State University and for Florida A&M University. Currently, he is an assistant professor of mathematics at Philadelphia University in Jordan. During his time at UAB, he coauthored papers and gave talks related to measure and integration theory.
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