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Introductory Analysis
ISBN-13:
9781351246736
Veröffentl:
2020
Seiten:
250
Autor:
John D. Ross
eBook Typ:
PDF
eBook Format:
EPUB
Kopierschutz:
0 - No protection
Sprache:
Englisch
Beschreibung:
Introductory Analysis: An Inquiry Approach aims to provide a self-contained, inquiry-oriented approach to undergraduate-level real analysis. The book is intended to be "inquiry-oriented'" in that as each major topic is discussed, details of the proofs are left to the student in a way that encourages an active approach to learning.
Prerequisites. P1. Exploring Mathematical Statements. P2. Proving Mathematical Statements. P3. Preliminary Content. Main Content. 1. Properties of R. 2. Accumulation Points and Closed Sets. 3. Open Sets and Open Covers. 4. Sequences and Convergence. 5. Subsequences and Cauchy Sequences. 6. Functions, Limits, and Continuity. 7. Connected Sets and the Intermediate Value Theorem. 8. Compact Sets. 9. Uniform Continuity. 10. Introduction to the Derivative. 11. The Extreme and Mean Value Theorems. 12. The Definite Integral: Part I. 13. The Definite Integral: Part II. 14. The Fundamental Theorem(s) of Calculus. 15. Series. Extended Explorations. E1. Function Approximation. E2. Power Series. E3. Sequences and Series of Functions. E4. Metric Spaces. E5. Iterated Functions and Fixed Point Theorems
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