1. Differential Calculus The mathematics of teeny little amounts Differential Calculus 1 

2. The Slope as a Limit Suppose we have measured the position versus time of a bicyclist using ultra-fancy laser equipment, etc. Differential Calculus 2 

3. Cyclist Position versus Time Plotting the data gives Differential Calculus 3 

4. Cyclist versus Time Differential Calculus 4 

5. Cyclist versus Time Differential Calculus 5 

6. Change in Time Let’s compute some values from our data. Differential Calculus 6 

7. We Want the Slope What we really need is the (exact) slope of the position curve at t = 2.7 seconds. Differential Calculus 7 

8. Limits Differential Calculus 8 

9. Limits: How to Actually Compute One Differential Calculus 9 

10. Taking It to the Limit Differential Calculus 10 

11. And The Answer Is Differential Calculus 11 

12. What Have We Done? Differential Calculus 12 

13. What a Lot of Work, Eh? We would be crazy don’t have to do this every time. Mostly we use a small set of standard results from either memory (or a book) plus a few composition rules. Differential Calculus 13 

14. Specific Derivatives Differential Calculus 14 

15. Exponentials and Logarithms Differential Calculus 15 

16. Exponentials and Logarithms Differential Calculus 16 

17. Exponentials and Logarithms Differential Calculus 17 

18. Exponentials and Logarithms Differential Calculus 18 

19. Exponentials and Logarithms Differential Calculus 19 

20. Composition Rules Composition rules are ways to break certain forms of complicated derivatives into expressions containing simpler derivatives. Differential Calculus 20 

21. Sum and Product Composition Rules Differential Calculus 21 

22. The Chain Composition Rule Differential Calculus 22 

23. More Chain Rule Differential Calculus 23 

24. Takeaway Derivatives are the (exact) slope of a curve. They are computed from a difference as the change in the arguments goes to zero. They are almost always computed by applying composition rules to the derivatives of some simple functions, or by using a reference book. Differential Calculus 24 

25. And That’s Differential Calculus Differential Calculus 25 