Yet Another Calculus Text
I intend this book to be, firstly, a introduction to calculus based on the hyperrealnumber system. In other words, I will use infinitesimal and infinite numbers freely. Just as most beginning calculus books provide no logical justification for the real number system, I will provide none for the hype...
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| Main Author: | |
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| Format: | Electronic eBook |
| Language: | English |
| Published: |
Greenville, South Carolina
Dan Sloughter
[2007]
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| Series: | Open textbook library.
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| Subjects: | |
| Online Access: | Access online version |
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Table of Contents:
- 1 Derivatives
- 1.1 The arrow paradox
- 1.2 Rates of change
- 1.3 The hyperreals
- 1.4 Continuous functions
- 1.5 Properties of continuous functions
- 1.6 The derivative
- 1.7 Properties of derivatives
- 1.8 A geometric interpretation of the derivative
- 1.9 Increasing, decreasing, and local extrema
- 1.10 Optimization
- 1.11 Implicit differentiation and rates of change
- 1.12 Higher-order derivatives
- 2 Integrals
- 2.1 Integrals
- 2.2 Definite integrals
- 2.3 Properties of definite integrals
- 2.4 The fundamental theorem of integrals
- 2.5 Applications of definite integrals
- 2.6 Some techniques for evaluating integrals
- 2.7 The exponential and logarithm functions
- Answers to ExercisesIndex