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Preface
1. 1 Introduction
2. 1.5 Exponential and Logarithmic Functions
3. 1.3 Trigonometric Functions
4. 2 Introduction
5. 2.1 A Preview of Calculus
6. 2.2 The Limit of a Function
7. 2.3 The Limit Laws
8. 2.6 Limits at Infinity and Asymptotes
9. 2.4 Continuity
10. 2.5 The Precise Definition of a Limit
11. Chapter 2 Review Exercises
12. 3 Introduction
13. 3.1 Defining the Derivative
14. 3.2 The Derivative as a Function
15. 3.3 Differentiation Rules
16. 3.4 Derivatives as Rates of Change
17. 3.5 Derivatives of Trigonometric Functions
18. 3.6 The Chain Rule
19. 3.7 Derivatives of Inverse Functions
20. 3.8 Implicit Differentiation
21. 3.9 Derivatives of Exponential and Logarithmic Functions
22. 4.1 Related Rates
23. Chapter 3 Review Exercises
24. 4 Introduction
25. 4.3 Maxima and Minima
26. 4.4 The Mean Value Theorem
27. 4.5 Derivatives and the Shape of a Graph
28. 4.6 Curve Sketching
29. 4.7 Applied Optimization Problems
30. 4.2 Linear Approximations and Differentials
31. 4.8 L’Hôpital’s Rule
32. 4.10 Antiderivatives
33. Chapter 4 Review Exercises
34. 5 Introduction
35. 5.1 Approximating Areas
36. 5.2 The Definite Integral
37. 5.3 The Fundamental Theorem of Calculus
38. 5.4 Integration Formulas and the Net Change Theorem
39. 5.5 Substitution
40. 5.6 Integrals Involving Exponential and Logarithmic Functions
41. 5.7 Integrals Resulting in Inverse Trigonometric Functions
42. Chapter 5 Review Exercises
Appendix
Table of Integrals
Table of Derivatives
Review of Pre-Calculus
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Calculus Volume 1 Copyright © 2016 by OSCRiceUniversity is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License, except where otherwise noted.