
- 362 pages
- English
- ePUB (mobile friendly)
- Available on iOS & Android
Mathematical Analysis Fundamentals
About this book
The author's goal is a rigorous presentation of the fundamentals of analysis, starting from elementary level and moving to the advanced coursework. The curriculum of all mathematics (pure or applied) and physics programs include a compulsory course in mathematical analysis. This book will serve as can serve a main textbook of such (one semester) courses. The book can also serve as additional reading for such courses as real analysis, functional analysis, harmonic analysis etc. For non-math major students requiring math beyond calculus, this is a more friendly approach than many math-centric options.- Friendly and well-rounded presentation of pre-analysis topics such as sets, proof techniques and systems of numbers- Deeper discussion of the basic concept of convergence for the system of real numbers, pointing out its specific features, and for metric spaces- Presentation of Riemann integration and its place in the whole integration theory for single variable, including the Kurzweil-Henstock integration- Elements of multiplicative calculus aiming to demonstrate the non-absoluteness of Newtonian calculus
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Information
Table of contents
- Cover image
- Title page
- Table of Contents
- Copyright
- Dedication
- Preface
- Chapter 1. Sets and Proofs
- Chapter 2. Numbers
- Chapter 3. Convergence
- Chapter 4. Point Set Topology
- Chapter 5. Continuity
- Chapter 6. Space C(E,E')
- Chapter 7. Differentiation
- Chapter 8. Bounded Variation
- Chapter 9. Riemann Integration
- Chapter 10. Generalizations of Riemann Integration
- Chapter 11. Transcendental Functions
- Chapter 12. Fourier Series and Integrals
- Bibliography