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Yet Another Calculus Text - A Short Introduction with Infinitesimals
This text is an introduction to calculus based on the hyperreal number system and uses infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, none are provided for the hyperreals. The text is aimed primarily at readers who already have some familiarity with calculus. Although the book does not explicitly assume any prerequisites beyond basic algebra and trigonometry, in practice the pace is too fast for most o
- Author
- Dan Sloughter
- Publisher
- Furman University
- Source
- LibreTexts
- License
- CC BY-NC-SA
- Language
- EN
- Category
- Basic Sciences
Contents· 21 sections
- 01: Derivatives
- 1.01: The Arrow Paradox
- 1.02: Rates of Change
- 1.03: The Hyperreals
- 1.04: Continuous Functions
- 1.05: Properties of Continuous Functions
- 1.06: The Derivatives
- 1.07: Properties of Derivatives
- 1.08: A Geometric Interpretation of the Derivatives
- 1.09: Increasing Decreasing and Local Extrema
- 1.10: Optimization
- 1.11: Implicit Differentiation and Rates of Change
- 1.12: Higher-Order Derivatives
- 02: Integrals
- 2.01: Integrals
- 2.02: Definite Integrals
- 2.03: Properties of Definite Integrals
- 2.04: The Fundamental Theorem of Integrals
- 2.05: Applications of Definite Integrals
- 2.06: Some Techniques for Evaluating Integrals
- 2.07: The Exponential and Logarithm Functions