John D. Ross, Kendall C. Richards

Introductory Analysis (eBook, PDF)

An Inquiry Approach

• Format: PDF

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis
• Seitenzahl: 250
• Erscheinungstermin: 31. Januar 2020
• Englisch
• ISBN-13: 9781351246736
• Artikelnr.: 58597203

Autorenporträt

John Ross is an Assistant Professor of Mathematics at Southwestern University. He earned his Ph.D. and M.A. in Mathematics from Johns Hopkins University, and his B.A. in Mathematics from St. Mary's College of Maryland. His research is in geometric analysis, answering questions about manifolds that arise under curvature flows. He enjoys overseeing undergraduate research, teaching in an inquiry-based format, biking to work, and hiking in Central Texas.

Kendall Richards is a Professor of Mathematics at Southwestern University. He earned his B.S. and M.A. in Mathematics from Eastern New Mexico University and his Ph.D. in Mathematics from Texas Tech University. He is inspired by working with students and the process of learning. His research pursuits have included questions involving special functions, inequalities, and complex analysis. He also enjoys long walks and a strong cup of coffee.

Inhaltsangabe

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