Book description
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
Table of contents
- Cover image
- Title page
- 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
- Abstract
- 12.1 Trigonometric Series
- 12.2 Riemann–Lebesgue Lemma
- 12.3 Dirichlet Kernels and Riemann’s Localization Lemma
- 12.4 Pointwise Convergence of Fourier Series
- 12.5* Fourier Series in Inner Product Spaces
- 12.6* Cesàro Summability and Fejér’s Theorem
- 12.7 Uniform Convergence of Fourier Series
- 12.8* Gibbs Phenomenon
- 12.9* Fourier Integrals
- Exercises
- Bibliography
Product information
- Title: Mathematical Analysis Fundamentals
- Author(s):
- Release date: March 2014
- Publisher(s): Elsevier
- ISBN: 9780128010501
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