# Introduction to Real Analysis: An Educational Approach

By: William C. Bauldry (author)Hardback

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WILLIAM C. BAULDRY, PhD , is Professor in the Department of Mathematical Sciences at Appalachian State University. Dr. Bauldry has published numerous articles in his areas of interest, which include the pedagogical uses of computer algebra systems and cryptography.

### Contents

Preface. Acknowledgments. 1 Elementary Calculus. 1.1 Preliminary Concepts. 1.2 Limits and Continuity. 1.3 Differentiation. 1.4 Integration. 1.5 Sequences and Series of Constants. 1.6 Power Series and Taylor Series. Summary. Exercises. Interlude: Fermat, Descartes, and theTangent Problem. 2 Introduction to Real Analysis. 2.1 Basic Topology of the Real Numbers. 2.2 Limits and Continuity. 2.3 Differentiation. 2.4 Riemann and Riemann-Stieltjes Integration. 2.5 Sequences, Series, and Convergence Tests. 2.6 Pointwise and Uniform Convergence. Summary. Exercises. Interlude: Euler and the "Basel Problem". 3 A Brief Introduction to Lebesgue Theory. 3.1 Lebesgue Measure and Measurable Sets. 3.2 The Lebesgue Integral. 3.3 Measure, Integral, and Convergence. 3.4 Littlewood's Three Principles. Summary. Exercises. Interlude: The Set of Rational Numbers isVery Large andVery Small. 4 Special Topics. 4.1 Modeling with Logistic Functions-Numerical Derivatives. 4.2 Numerical Quadrature. 4.3 Fourier Series. 4.4 Special Functions-The Gamma Function. 4.5 Calculus Without Limits: Differential Algebra. Summary. Exercises. Appendix A: Definitions and Theorems of Elementary Real Analysis. A.1 Limits. A.2 Continuity. A.3 The Derivative. A.4 Riemann Integration. A.5 Riemann-Stieltjes Integration. A.6 Sequences and Series of Constants. A.7 Sequences and Series of Functions. Appendix B: A Very Brief Calculus Chronology. Appendix C: Projects in Real Analysis. C.1 Historical Writing Projects. C.2 Induction Proofs: Summations, Inequalities, and Divisibility. C.3 Series Rearrangements. C.4 Newton and the Binomial Theorem. C.5 Symmetric Sums of Logarithms. C.6 Logical Equivalence: Completeness of the Real Numbers. C.7 Vitali's Nonmeasurable Set. C.8 Sources for Real Analysis Projects. C.9 Sources for Projects for Calculus Students. Bibliography. Index.

### Product Details

• publication date: 31/07/2009
• ISBN13: 9780470371367
• Format: Hardback
• Number Of Pages: 262
• ID: 9780470371367
• weight: 506
• ISBN10: 0470371366

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