## Description

Solutions Manual – Analysis with an Introduction to Proof, 6th edition by Steven R. Lay

Table of Contennts

**1. Logic and Proof**

- 1.1 Logical Connectives
- 1.2 Quantifiers
- 1.3 Techniques of Proof: I
- 1.4 Techniques of Proof: II

**2. Sets and Functions**

- 2.1 Basic Set Operations
- 2.2 Relations
- 2.3 Functions
- 2.4 Cardinality
- 2.5 Axioms for Set Theory

**3. The Real Numbers**

- 3.1 Natural Numbers and Induction
- 3.2 Ordered Fields
- 3.3 The Completeness Axiom
- 3.4 Topology of the Real Numbers
- 3.5 Compact Sets
- 3.6 Metric Spaces

**4. Sequences**

- 4.1 Convergence
- 4.2 Limit Theorems
- 4.3 Monotone Sequences and Cauchy Sequences
- 4.4 Subsequences

**5. Limits and Continuity**

- 5.1 Limits of Functions
- 5.2 Continuous Functions
- 5.3 Properties of Continuous Functions
- 5.4 Uniform Continuity
- 5.5 Continuity in Metric Space

**6. Differentiation**

- 6.1 The Derivative
- 6.2 The Mean Value Theorem
- 6.3 L’Hôspital’s Rule
- 6.4 Taylor’s Theorem

**7. Integration**- 7.1 The Riemann Integral
- 7.2 Properties of the Riemann Integral
- 7.3 The Fundamental Theorem of Calculus

**8. Infinite Series**

- 8.1 Convergence of Infinite Series
- 8.2 Convergence Tests
- 8.3 Power Series

**9. Sequences and Series of Functions**

- 9.1 Pointwise and Uniform Convergence
- 9.2 Application of Uniform Convergence
- 9.3 Uniform Convergence of Power Series

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