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Calculus

This free online calculus course teaches introductory methods including derivatives, related rates, and integrals. The course consists of 55 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.
Calculus

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

Practice Problems


​Derivatives

19. Differentiation explained
20. Power rule examples #1
21. Power rule examples #2
22. Scalar rule and the derivative of a constant
23. Addition rule examples
24. Some derivatives that you should know
25. Product rule examples #1
26. Product rule examples #2
27. Quotient rule examples #1
28. Quotient Rule examples #2
29. Chain rule examples #1
30. Chain rule examples #2
31. Higher derivatives and curve sketching
32. Higher order derivatives examples 
33. Logarithmic differentiation examples
34. Implicit differentiation example #1

35. Implicit differentiation example #2
36. Implicit differentiation example #3

37. Slope of a curve at a given point
38. Equation of the tangent line to a curve at a given point
39. Equation of the normal line to a curve at a given point
40. Newtons method explained
41. Newtons method example
​
Practice Problems


​Applications of Differentiation

42. Throwing a stone up off of a cliff
43. Related Rates: A ladder slides down a wall
44. Related Rates: Two boats sail away from each other at an angle of 90°
45. Related Rates: A balloon fills with a gas
46. Related Rates: Water fills a conical tank
47. Related Rates: How fast does your shadow grow while walking away from a lamp post


Optimization

48. How to fit the biggest possible square inside of a circle
49. How to fit the biggest possible rectangle inside of an ellipse
50. How to maximize the surface area of a can with a given volume
51. How to minimize the surface area of a box of a certain volume
52. Minimize the time to swim across a river then walk along the shore


Integrals

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



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Recommended Books

Calculus Study Guide
Calculus Book


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  • Dynamics
  • Linear Algebra
  • Mechanics of Materials
  • Project Management
  • Statics
  • Structural Analysis
  • Home
  • C++ Programming
  • Circuits
  • Calculus 1
  • Calculus 2
  • Chemistry
  • Differential Equations
  • Dynamics
  • Linear Algebra
  • Mechanics of Materials
  • Project Management
  • Statics
  • Structural Analysis