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Check for Availabilityout of stock. Click on the button below to search for this title in other formats.  Introduction to Real Analysis
Synopses & ReviewsBook News Annotation:This textbook is designed for a one-year course in real analysis at
the junior or senior level. An understanding of real analysis is
necessary for the study of advanced topics in mathematics and the
physical sciences, and is helpful to advanced students of
engineering, economics, and the social sciences. Stoll, who teaches
at the U. of South Carolina, presents examples and counterexamples to
illustrate topics such as the structure of point sets, limits and
continuity, differentiation, and orthogonal functions and Fourier
series. The second edition includes a self-contained proof of
Lebesgue's theorem and a new appendix on logic and proofs.
Annotation c. Book News, Inc., Portland, OR (booknews.com) Description:Includes bibliographical references (p. 522) and indexes. Table of Contents(Each chapter concludes with “Notes”, “Miscellaneous Exercises”, and a “Supplemental Reading”.)
1. The Real Number System.
Sets and Operations on Sets.
Functions.
Mathematical Induction.
The Least Upper Bound Property.
Consequences of the Least Upper Bound Property.
Binary and Ternary Expansions.
Countable and Uncountable Sets.
2. Sequence Of Real Numbers.
Convergent Sequences.
Limit Theorems.
Monotone Sequences.
Subsequences and the Bolzano-Weierstrass Theorem.
Limit Superior and Inferior of a Sequence.
Cauchy Sequences.
Series of Real Numbers.
3. Structure Of Point Sets.
Open and Closed Sets.
Compact Sets.
The Cantor Set.
4. Limits And Continuity.
Limit of a Function.
Continuous Functions.
Uniform Continuity.
Monotone Functions and Discontinuities.
5. Differentiation.
The Derivative.
The Mean Value Theorem.
L'Hôpital's Rule.
Newton's Method.
6. The Riemann And Riemann-Stieltjes Integral.
The Riemann Integral.
Properties of the Riemann Integral.
Fundamental Theorem of Calculus.
Improper Riemann Integrals.
The Riemann-Stieltjes Integral.
Numerical Methods.
Proof of Lebesgue's Theorem.
7. Series of Real Numbers.
Convergence Tests.
The Dirichlet Test.
Absolute and Conditional Convergence.
Square Summable Sequences.
8. Sequences And Series Of Functions.
Pointwise Convergence and Interchange of Limits.
Uniform Convergence.
Uniform Convergence and Continuity.
Uniform Convergence and Integration.
Uniform Convergence and Differentiation.
The Weierstrass Approximation Theorem.
Power Series Expansion.
The Gamma Function.
9. Orthogonal Functions And Fourier Series.
Orthogonal Functions.
Completeness and Parseval's Equality.
Trigonometric and Fourier Series.
Convergence in the Mean of Fourier Series.
Pointwise Convergence of Fourier Series.
10. Lebesgue Measure And Integration.
Introduction to Measure.
Measure of Open Sets; Compact Sets.
Inner and Outer Measure; Measurable Sets.
Properties of Measurable Sets.
Measurable Functions.
The Lebesgue Integral of a Bounded Function.
The General Lebesgue Integral.
Square Integrable Functions.
Appendix: Logic and Proofs.
Propositions and Connectives.
Rules of Inference.
Mathematical Proofs.
Use of Quantifiers.
Supplemental Reading.
Bibliography.
Hints and Solutions to Selected Exercises.
Notation Index.
Index. What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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