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Introduction to Calculus

1. What Is Calculus?

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This course is designed to follow the order of topics presented in a traditional calculus course. Each topic builds on the previous one. It is recommended that you start with Lesson 1 and progress through the video lessons, working through each problem session and taking each quiz in the order it appears in the table of contents.

- Watch all lesson and problem session videos in the course.
- Complete all 10 course quizzes with a passing grade of 60% or better. (It is OK to retry any of the quizzes.)

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1. What Is Calculus?

2. Functions

3. The Elementary Functions

4. The Limit of a Function

5. The Laws of Limits

Problem Session 1

6. Continuity

7. Derivatives and Rates of Change

8. The Derivative as a Function

Problem Session 2

9. Differentiation Formulas

10. Derivatives of Trigonometric Functions

11. The Chain Rule

12. Implicit Differentiation

Problem Session 3

13. Rates of Change in the Sciences

14. Related Rates

15. Linear Approximations

Problem Session 4

16. Maxima and Minima

17. The Mean Value Theorem

18. Derivatives and the Shape of Graphs

19. Asymptotes

20. Curve Sketching

Problem Session 5

21. Optimization

22. Antiderivatives

23. Riemann Sums

Problem Session 6

24. The Definite Integral

25. The Fundamental Theorem of Calculus

26. Indefinite Integrals

27. The Substitution Rule

Problem Session 7

28. Areas between Curves

29. Volumes of Solids

30. Volumes by Cylindrical Shells

Problem Session 8

31. Average Value of a Function

32. Approximate Integration

33. Exponential Functions

34. Logarithmic Functions

Problem Session 9

35. L'Hospital's Rule

36. Slope Fields and Euler's Method

37. Separable Differential Equations

Problem Session 10

38. Calculus and Programming

39. Sample Calculus Exam, Part 1

40. Sample Calculus Exam, Part 2

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