Analysis with an Introduction to Proof, 6th edition

Published by Pearson (October 31, 2023) © 2024

  • Steven R. Lay Lee University
  • Richard G Ligo Gannon University
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Analysis with an Introduction to Proof eases your transition to advanced mathematics, building the foundation that is essential to help you succeed in real analysis (often considered the most difficult course in the undergrad math curriculum). It introduces logic and emphasizes the structure and nature of the arguments used, helping you move from earlier, computationally oriented courses to working with proofs. Helpful examples and practice problems, numerous drawings, and selected hints/answers make the material both readable and user friendly.

The 6th Edition welcomes new co-author Richard Ligo, adds new GeoGebra-powered Interactive Figures, expands on the text's hallmark strengths, and more.

  • 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
Glossary of Key Terms
References
Hints for Selected Exercises
Index

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