This free online calculus course teaches introductory methods including derivatives, related rates, and integrals. The course consists of 46 tutorials which cover the material of a typical single variable calculus course (calculus I) at the university level.

In order to gain a comprehensive understanding of the subject, you should start at the top and work your way down the list. That way you will start learning the most basic concepts first and build off of those as you progress through the course.

Basic Function Introduction/Review

1. Functions, domain, and range explained
2. How to complete the square for sketching square functions
3. Find the roots of a polynomial (cubic functions)
4. Square root functions
5. Cube root functions
6. Absolute value functions
7. Exponential functions
8. Log functions and the natural log
9. Uncategorized functions (the most common kind you will encounter)
10. One-to-one functions
11. Inverse functions
12. Constant Functions
13. Drawing functions with a reduced domain
14. Composite functions
15. Determine if a function is even or odd

Limits

16. Limits explained
17. Limit examples
18. One-sided limits and limits that don't exist

Derivatives

19. Differentiation explained
20. Power rule examples
21. Scalar rule and the derivative of a constant
22. Addition rule examples
23. Some derivatives that you should know
24. Product rule examples
25. Quotient rule examples
26. Chain rule examples
27. Higher derivatives and curve sketching
28. Logarithmic differentiation
29. Implicit differentiation
30. Find the normal to a curve
31. Newtons method explained
32. Newtons method example

Applications of Differentiation

33. Throwing a stone up off of a cliff
34. Related Rates: A ladder slides down a wall
35. Related Rates: Two boats sail away from each other at an angle of 90°
36. Related Rates: A balloon fills with a gas
37. Related Rates: Water fills a conical tank
38. Related Rates: How fast does your shadow grow while walking away from a lamp post

Optimization

39. How to fit the biggest possible square inside of a circle
40. How to fit the biggest possible rectangle inside of an ellipse
41. How to maximize the surface area of a can with a given volume
42. How to minimize the surface area of a box of a certain volume
43. Minimize the time to swim across a river then walk along the shore

Integrals

44. Guessing anti-derivatives (power rule examples)
45. Using definite integrals to find the area under a curve
46. How to find the area enclosed between two curves

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