Real Analysis: Foundations and Functions of One Variable (Undergraduate Texts in Mathematics) - Softcover

Laczkovich, Miklós; Sós, Vera T.

Softcover

ISBN 10: 1493942220 ISBN 13: 9781493942220

Verlag: Springer, 2016

Inhaltsangabe

<P>BASED ON COURSES GIVEN AT EÖTVÖS LORÁND UNIVERSITY (HUNGARY) OVER THE PAST 30 YEARS, THIS INTRODUCTORY TEXTBOOK DEVELOPS THE CENTRAL CONCEPTS OF THE ANALYSIS OF FUNCTIONS OF ONE VARIABLE — SYSTEMATICALLY, WITH MANY EXAMPLES AND ILLUSTRATIONS, AND IN A MANNER THAT BUILDS UPON, AND SHARPENS, THE STUDENT’S MATHEMATICAL INTUITION. THE BOOK PROVIDES A SOLID GROUNDING IN THE BASICS OF LOGIC AND PROOFS, SETS, AND REAL NUMBERS, IN PREPARATION FOR A STUDY OF THE MAIN TOPICS: LIMITS, CONTINUITY, RATIONAL FUNCTIONS AND TRANSCENDENTAL FUNCTIONS, DIFFERENTIATION, AND INTEGRATION. NUMEROUS APPLICATIONS TO OTHER AREAS OF MATHEMATICS, AND TO PHYSICS, ARE GIVEN, THEREBY DEMONSTRATING THE PRACTICAL SCOPE AND POWER OF THE THEORETICAL CONCEPTS TREATED.</P><P>IN THE SPIRIT OF LEARNING-BY-DOING, <I>REAL ANALYSIS</I> INCLUDES MORE THAN 500 ENGAGING EXERCISES FOR THE STUDENT KEEN ON MASTERING THE BASICS OF ANALYSIS. THE WEALTH OF MATERIAL, AND MODULAR ORGANIZATION, OF THE BOOK MAKE IT ADAPTABLE AS A TEXTBOOK FOR COURSES OF VARIOUS LEVELS; THE HINTS AND SOLUTIONS PROVIDED FOR THE MORE CHALLENGING EXERCISES MAKE IT IDEAL FOR INDEPENDENT STUDY.</P>

Über diesen Titel

Críticas

“This book is written to be accessible to the competent university student. ... The book is consistent in addressing the classical analysis of real functions of one real variable, and it can serve as an introduction to monographs of complex functions, functional analysis and differential equations, upon which it touches occasionally. It can also serve as an introduction to Lebesgue integration or to generalized functions, which are not mentioned.” (Luis Manuel Braga de Costa Campos, Mathematical Reviews, December, 2016)

Reseña del editor

Based on courses given at Eötvös Loránd University (Hungary) over the past 30 years, this introductory textbook develops the central concepts of the analysis of functions of one variable ― systematically, with many examples and illustrations, and in a manner that builds upon, and sharpens, the student’s mathematical intuition. The book provides a solid grounding in the basics of logic and proofs, sets, and real numbers, in preparation for a study of the main topics: limits, continuity, rational functions and transcendental functions, differentiation, and integration. Numerous applications to other areas of mathematics, and to physics, are given, thereby demonstrating the practical scope and power of the theoretical concepts treated.

In the spirit of learning-by-doing, Real Analysis includes more than 500 engaging exercises for the student keen on mastering the basics of analysis. The wealth of material, and modular organization, of the book make it adaptable as a textbook for courses of various levels; the hints and solutions provided for the more challenging exercises make it ideal for independent study.

Details zur Ausgabe

• Verlag: Springer
• Erscheinungsdatum: 2016
• ISBN 10: 1493942220
• ISBN 13: 9781493942220
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 500