An Invitation to Real Analysis
eBook - ePub

An Invitation to Real Analysis

  1. English
  2. ePUB (mobile friendly)
  3. Available on iOS & Android
eBook - ePub

An Invitation to Real Analysis

About this book

Adopting a student-centered approach, this book anticipates and addresses the common challenges that students face when learning abstract concepts like limits, continuity, and inequalities. The text introduces these concepts gradually, giving students a clear pathway to understanding the mathematical tools that underpin much of modern science and technology. In addition to its focus on accessibility, the book maintains a strong emphasis on mathematical rigor. It provides precise, careful definitions and explanations while avoiding common teaching pitfalls, ensuring that students gain a deep understanding of core concepts, and blending algebraic and geometric perspectives to help students see the full picture. The theoretical results presented in the book are consistently applied to practical problems. By providing a clear and supportive introduction to real analysis, the book equips students with the tools they need to confidently engage with both theoretical mathematics and its wide array of practical applications.

Features

  • Student-Friendly Approach making abstract concepts relatable and engaging
  • Balanced Focus combining algebraic and geometric perspectives
  • Comprehensive Coverage: Covers a full range of topics, from real numbers and sequences to metric spaces and approximation theorems, while carefully building upon foundational concepts in a logical progression
  • Emphasis on Clarity: Provides precise explanations of key mathematical definitions and theorems, avoiding common pitfalls in traditional teaching
  • Perfect for a One-Semester Course: Tailored for a first course in real analysis
  • Problems, exercises and solutions

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Yes, you can access An Invitation to Real Analysis by Andrew D. Hwang in PDF and/or ePUB format, as well as other popular books in Mathematics & Functional Analysis. We have over one million books available in our catalogue for you to explore.

Information

Table of contents

  1. Cover Page
  2. Half-Title Page
  3. Series Page
  4. Title Page
  5. Copyright Page
  6. Dedication Page
  7. Contents
  8. To the Instructor
  9. To the Student
  10. 1 Logic and Sets
  11. 2 Natural Numbers and Induction
  12. 3 Real Numbers
  13. 4 The Real Number Line
  14. 5 Functions
  15. 6 Sequences
  16. 7 Infinite Series
  17. 8 Continuous Functions
  18. 9 Integration
  19. 10 Differentiation
  20. 11 The Fundamental Theorems of Calculus
  21. 12 Exponential Functions
  22. 13 Circular Functions
  23. 14 Complex Numbers
  24. 15 Linear Spaces
  25. 16 Metric Spaces
  26. 17 Approximation Theorems
  27. A Solutions to Selected Exercises
  28. Bibliography
  29. Index