Understanding Infinity: The Mathematics of Infinite Processes - Brossura

Gardiner, A.

Brossura

ISBN 10: 048642538X ISBN 13: 9780486425382

Casa editrice: Dover Pubns, 2003

Riassunto

Conceived by the author as an introduction to "why the calculus works" (otherwise known as "analysis"), this volume represents a critical reexamination of the infinite processes encountered in elementary mathematics. Part I presents a broad description of the coming parts, and Part II offers a detailed examination of the infinite processes arising in the realm of number--rational and irrational numbers and their representation as infinite decimals. Most of the text is devoted to analysis of specific examples. Part III explores the extent to which the familiar geometric notions of length, area, and volume depend on infinite processes. Part IV defines the evolution of the concept of functions by examining the most familiar examples--polynomial, rational, exponential, and trigonometric functions. Exercises form an integral part of the text, and the author has provided numerous opportunities for students to reinforce their newly acquired skills. Unabridged republication of Infinite Processes as published by Springer-Verlag, New York, 1982. Preface. Advice to the Reader. Index.

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Contenuti

PART I FROM CALCULUS TO ANALYSIS CHAPTER I.1 What's Wrong with the Calculus? CHAPTER I.2 Growth and Change in Mathematics PART II NUMBER CHAPTER II.1 Mathematics: Rational or Irrational? CHAPTER II.2 Constructive and Non-constructive Methods in Mathematics "CHAPTER II.3 Common Measures, Highest Common Factors and the Game of Euclid" CHAPTER II.4 Sides and Diagonals of Regular Polygons CHAPTER II.5 Numbers and Arithmetic?A Quick Review CHAPTER II.6 Infinite Decimals (Part 1) CHAPTER II.7 Infinite Decimals (Part 2) CHAPTER II.8 Recurring Nines CHAPTER II.9 Fractions and Recurring Decimals CHAPTER II.10 The Fundamental Property of Real Numbers CHAPTER II.11 The Arithmetic of Infinite Decimals CHAPTER II.12 Reflections on Recurring Themes CHAPTER II.13 Continued Fractions PART III GEOMETRY CHAPTER III.1 Numbers and Geometry CHAPTER III.2 The Role of Geometrical Intuition CHAPTER III.3 Comparing Areas CHAPTER III.4 Comparing Volumes CHAPTER III.5 Curves and Surfaces PART IV FUNCTIONS CHAPTER IV.1 What Is a Number? CHAPTER IV.2 What Is a Function? CHAPTER IV.3 What Is an Exponential Function? Index Errata

Dettagli dell'edizione

• Editore: Dover Pubns
• Data di pubblicazione: 2003
• Lingua: Inglese
• ISBN 10: 048642538X
• ISBN 13: 9780486425382
• Rilegatura: Copertina flessibile
• Numero di pagine: 320
• Contatto del produttore: non disponibile
• Persona responsabile: Soc. Agr. La Raia Ss; http://www.la-raia.it; ; Strada Monterotondo, 79; Novi Ligure; 15067; Italia