Elementary Real Analysis is a core course in nearly all mathematics departments throughout the world. It enables students to develop a deep understanding of the key concepts of calculus from a mature perspective. Elements of Real Analysis is a student-friendly guide to learning all the important ideas of elementary real analysis, based on the author's many years of experience teaching the subject to typical undergraduate mathematics majors. It avoids the compact style of professional mathematics writing, in favor of a style that feels more comfortable to students encountering the subject for the first time. It presents topics in ways that are most easily understood, yet does not sacrifice rigor or coverage.
In using this book, students discover that real analysis is completely deducible from the axioms of the real number system. They learn the powerful techniques of limits of sequences as the primary entry to the concepts of analysis, and see the ubiquitous role sequences play in virtually all later topics. They become comfortable with topological ideas, and see how these concepts help unify the subject. Students encounter many interesting examples, including "pathological" ones, that motivate the subject and help fix the concepts. They develop a unified understanding of limits, continuity, differentiability, Riemann integrability, and infinite series of numbers and functions.
Features & Benefits
- Student-friendly style of exposition.
- Comprehensive coverage of key material
- Chapters and sections presented in a natural and logical sequence.
- Flexible format allows instructors to tailor the text to fit their course needs.
- Generous exercies, graded from routine to more difficult.
An ideal text for undergraduate and graduate-level courses in Elementary Real Analysis which is an essential part of the preparation of every math teacher, particularly those going on to teach Calculus.
To The Student
To The Instructor
Chapter 1 The Real Number System
Chapter 2 Sequences
Chapter 3 Topology of the Real Number System
Chapter 4 Limits of Functions
Chapter 5 Continuous Functions
Chapter 6 Differentiable Functions
Chapter 7 The Riemann Integral
Chapter 8 Infinite Series of Real Numbers
Chapter 9 Sequences and Series of Functions
Appendix A Logic and Proofs
Appendix B Sets and Functions
Appendix C Answers and Hints for Selected Exercises
Glossary of Symbols
Charles G. Denlinger
Charles G. Denlinger is Emeritus Professor of Mathematics at Millersville University, of the Pennsylvania State System of Higher Education. He retired from MU in 2005 after 41 years of service, including eleven years as Chair of the Department of Mathematics. His academic credentials include the Ph.D. degree in Mathematics from Michigan State University in 1971, the M.S. in Mathematics from the University of Illinois in 1963, and the B.A. from Elizabethtown (PA) College in 1961. He has previously co-authored two calculus textbooks with Bernard Kolman.
Professor Denlinger enjoys teaching mathematics at all levels, but especially loves to make complicated mathematics understandable to serious, hard-working students. Seeing the light dawn in the face of an appreciative student is intensely satisfying to him as a teacher. His favorite undergraduate course to teach was, of course, Real Analysis - closely followed by Linear Algebra. In addition to Calculus and more elementary courses, he also occasionally taught Abstract Algebra, Number Theory, Geometry, and General Topology. He also taught in Millersville’s masters degree program in Mathematics Education. Fortunately for him and his students, he was never assigned to teach a statistics course.
In retirement, “Chuck” continues to study real analysis and its history, although at a much reduced pace. He and his wife Gloria love traveling to visit other countries and cultures. They share a deep appreciation for classical music, and are active supporters of musical organizations. They are also involved in their church and its service to the community. But their deepest commitment is to their family. They have a son and a daughter, as well as two grandchildren, with hopefully more on the way.