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Elements of Real Analysis. Charles G. 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. 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. Logic and Proofs. Sets and Functions. Answers and Hints for Selected Exercises. Glossary of Symbols. Elements of Real Analysis Charles G. Chapter 1 The Real Number System.
Elements Of Real Analysis
Charles G. He retired from MU in after 41 years of service, including eleven years as Chair of the Department of Mathematics. His academic credentials include the Ph. 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.
Elements of Real Analysis
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