## Description

**Solutions Manual – Analysis with an Introduction to Proof, 5th edition by Steven R. Lay **

## Table of Contents

**Logic and Proof**- Section 1. Logical Connectives
- Section 2. Quantifiers
- Section 3. Techniques of Proof: I
- Section 4. Techniques of Proof: II

**Sets and Functions**- Section 5. Basic Set Operations
- Section 6. Relations
- Section 7. Functions
- Section 8. Cardinality
- Section 9. Axioms for Set Theory(Optional)

**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)

**Sequences**- Section 16. Convergence
- Section 17. Limit Theorems
- Section 18. Monotone Sequences and Cauchy Sequences
- Section 19. Subsequences

**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)

**Differentiation**- Section 25. The Derivative
- Section 26. The Mean Value Theorem
- Section 27. L’Hôpital’s Rule
- Section 28. Taylor’s Theorem

**Integration**- Section 29. The Riemann Integral
- Section 30. Properties of the Riemann Integral
- Section 31. The Fundamental Theorem of Calculus

**Infinite Series**- Section 32. Convergence of Infinite Series
- Section 33. Convergence Tests
- Section 34. Power Series

**Sequences and Series of Functions**- Section 35. Pointwise and uniform Convergence
- Section 36. Application of Uniform Convergence
- Section 37. Uniform Convergence of Power Series

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