1. Logic and Proof Section 1. Logical Connectives Section 2. Quantifiers Section 3. Techniques of Proof: I Section 4. Techniques of Proof: II   2. Sets and Functions Section 5. Basic Set Operations Section 6. Relations Section 7. Functions Section 8. Cardinality Section 9. Axioms for Set Theory(Optional)   3. The Real Numbers Section 10. Natural Numbers and Induction Section 11. Ordered Fields Section 12. The Completeness Axiom Section 13. Topology of the Reals Section 14. Compact Sets Section 15. Metric Spaces (Optional)   4. Sequences Section 16. Convergence Section 17. Limit Theorems Section 18. Monotone Sequences and Cauchy Sequences Section 19. Subsequences   5. Limits and Continuity Section 20. Limits of Functions Section 21. Continuous Functions Section 22. Properties of Continuous Functions Section 23. Uniform Continuity Section 24. Continuity in Metric Space (Optional)   6. Differentiation Section 25. The Derivative Section 26. The Mean Value Theorem Section 27. L'Hospital's Rule Section 28. Taylor's Theorem   7. Integration Section 29. The Riemann Integral Section 30. Properties of the Riemann Integral Section 31. The Fundamental Theorem of Calculus   8. Infinite Series Section 32. Convergence of Infinite Series Section 33. Convergence Tests Section 34. Power Series   9. Sequences and Series of Functions Section 35. Pointwise and uniform Convergence Section 36. Application of Uniform Convergence Section 37. Uniform Convergence of Power Series   Glossary of Key Terms References Hints for Selected Exercises Index    

More than 250 true/false questions are unique to this text and tied directly to the narrative; these are perfect for stimulating class discussion and debate. Carefully worded to anticipate common student errorsEncourage critical thinking and promote careful reading of the textThe justification for a “false" answer is often an example that the students can add to their growing collection of counterexamples.More than 100 practice problems throughout the text provide a simple problem for students to apply what they have just read. Answers are provided just prior to the exercises for reinforcement and for students to check their understanding.Exceptionally high-quality drawings illustrate key ideas.Numerous examples and more than 1,000 exercises give the breadth and depth of practice that students need to learn and master the material.Fill-in-the-blank proofs guide students in the art of writing proofs.Glossary of Key Terms at the end of the book includes 180 key terms with the meaning and page number where each is introduced, providing an invaluable reference when studying, or for future courses.Review of Key Terms after each section emphasizes the importance of definitions and language in mathematics and helps students organize their studying.

Some proofs have been simplified and there are several new examples and illustrations.More than 200 new exercises provide more of the practice that students need to master the material.The definition of a convergent sequence has been changed to include the more traditional requirement that the number limiting the indices should be a natural number (rather than a real number). This emphasizes the Archimedean property of the real numbers.Animated PowerPoint Presentations are now available for all sections in the text. More than just an outline of each lesson, these were created by the author for use in his own classroom.