Infinite Processes Background to Analysis
What shall we say of this metamorphosis in passing from finite to infinite? Galileo, Two New Sciences As its title suggests, this book was conceived as a prologue to the study of "Why the calculus works"--otherwise known as analysis. It is in fact a critical reexamination of the infinite p...
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| Format: | eBook |
| Language: | English |
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New York, NY
Springer New York
1982, 1982
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| Edition: | 1st ed. 1982 |
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| Online Access: | |
| Collection: | Springer Book Archives -2004 - Collection details see MPG.ReNa |
Table of Contents:
- I From Calculus to Analysis
- I.1 What’s Wrong with the Calculus?
- I.2 Growth and Change in Mathematics
- II Number
- II.1 Mathematics: Rational or Irrational?
- II.2 Constructive and Non-constructive Methods in Mathematics
- II.3 Common Measures, Highest Common Factors and the Game of Euclid
- II.4 Sides and Diagonals of Regular Polygons
- II.5 Numbers and Arithmetic—A Quick Review
- II.6 Infinite Decimals (Part 1)
- II.7 Infinite Decimals (Part 2)
- II.8 Recurring Nines
- II.9 Fractions and Recurring Decimals
- II.10 The Fundamental Property of Real Numbers
- II.11 The Arithmetic of Infinite Decimals
- II.12 Reflections on Recurring Themes
- II.13 Continued Fractions
- III Geometry
- III.1 Numbers and Geometry
- III.2 The Role of Geometrical Intuition
- III.3 Comparing Areas
- III.4 Comparing Volumes
- III.5 Curves and Surfaces
- IV Functions
- IV.1 What Is a Number?
- IV.2 What Is a Function?
- IV.3 What Is an Exponential Function?