A Modern Introduction to Mathematical Analysis 1st Edition by Alessandro Fonda ISBN 3031237137 9783031237133

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Product details:

ISBN 10: 3031237137

ISBN 13: 9783031237133 

Author: Alessandro Fonda 

This textbook presents all the basics for the first two years of a course in mathematical analysis, from the natural numbers to Stokes-Cartan Theorem.
The main novelty which distinguishes this book is the choice of introducing the Kurzweil-Henstock integral from the very beginning. Although this approach requires a small additional effort by the student, it will be compensated by a substantial advantage in the development of the theory, and later on when learning about more advanced topics.
The text guides the reader with clarity in the discovery of the many different subjects, providing all necessary tools – no preliminaries are needed. Both students and their instructors will benefit from this book and its novel approach, turning their course in mathematical analysis into a gratifying and successful experience.

Table of contents:

Part I. The Basics of Mathematical Analysis
1. Sets of Numbers and Metric Spaces
2. Continuity
3. Limits
4. Compactness and Completeness
5. Exponential and Circular Functions
Part II. Differential and Integral Calculus in ℝ
6. The Derivative
7. The Integral
Part III. Further Developments
8. Numerical Series and Series of Functions
9. More on the Integral
Part IV. Differential and Integral Calculus in ℝ N
10. The Differential
11. The Integral
12. Differential Forms

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