Understanding Analysis

Nonfiction, Science & Nature, Mathematics, Mathematical Analysis, Calculus
Cover of the book Understanding Analysis by Stephen Abbott, Springer New York
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Stephen Abbott ISBN: 9781493927128
Publisher: Springer New York Publication: May 19, 2015
Imprint: Springer Language: English
Author: Stephen Abbott
ISBN: 9781493927128
Publisher: Springer New York
Publication: May 19, 2015
Imprint: Springer
Language: English

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of  them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.

Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation ­ Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

This lively introductory text exposes the student to the rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of  them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is much better prepared to understand what constitutes a proper mathematical proof and how to write one.

Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises join a selection of the best exercises from the first edition, and three more project-style sections have been added. Investigations of Euler’s computation of ζ(2), the Weierstrass Approximation ­ Theorem, and the gamma function are now among the book’s cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.

More books from Springer New York

Cover of the book Celiac Disease by Stephen Abbott
Cover of the book Cannabinoid Modulation of Emotion, Memory, and Motivation by Stephen Abbott
Cover of the book Diseases of the Sinuses by Stephen Abbott
Cover of the book Forest BioEnergy Production by Stephen Abbott
Cover of the book Environmental Sensing by Stephen Abbott
Cover of the book Scanning Probe Microscopy of Functional Materials by Stephen Abbott
Cover of the book Biosynthesis and Molecular Genetics of Fungal Secondary Metabolites by Stephen Abbott
Cover of the book Bifurcation Theory of Functional Differential Equations by Stephen Abbott
Cover of the book Digital Imaging Systems for Plain Radiography by Stephen Abbott
Cover of the book Brain Theory From A Circuits And Systems Perspective by Stephen Abbott
Cover of the book Alcohol Use Disorders and the Lung by Stephen Abbott
Cover of the book Fundamentals of Shallow Water Acoustics by Stephen Abbott
Cover of the book Helium Ion Microscopy by Stephen Abbott
Cover of the book Atlas of Ultrasound-Guided Procedures in Interventional Pain Management by Stephen Abbott
Cover of the book Disruptive Logic Architectures and Technologies by Stephen Abbott
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy