Notes for Math 1A, fall 2013

Use these notes at your own risk. I am writing them in order to clarify for myself what I covered (or intended to cover) in class, as well as to elaborate on points that I did not have time to cover in class. Of course, I very much hope that they can be useful to you. I welcome any corrections or suggestions.

Note that the dates and lecture numbers correspond to sections meeting on Monday, Wednesday and Friday, although I teach on Tuesday and Thursday. I organize it this way to match the division of the homework problems and course material.

Lecture notes

1. Introductions (M 9 September)
2. Average rate of change (W 11 September)
3. Introduction to limits (F 13 September)

4. Continuity I (M 16 September)
5. Continuity II (W 18 September)
6. Derivatives (F 20 September)

7. The derivative as a function (M 23 September)
8. What f' says about f (W 25 September)

Material for first midterm ends here.

9. Differentiating polynomials and exponentials (F 27 September)

10. Linear approximation (M 30 September)
11. Extrema (W 2 October)
12. Sketching functions (F 4 October)

13. Optimization I (M 7 October)
14. Products, quotients, and trig functions (W 9 October)
15. Optimization II (F 11 October)

(No class M 14 October)
16. The Chain rule (W 16 October)
17. Implicit Differentiation (F 18 October)

18. Infinite limits (M 21 October)
19. Limits to infinity (W 23 October)
20. Further graphing (F 25 October)

21. Logarithmic differentiation (M 28 October)
22. Related rates (W 30 October)
Exam 2 Review Review problems Answers

23. L'Hôpital's rule (F 1 November)
24. Indeterminate forms (W 6 November)
25. Anti-derivatives (F 8 November)

26. Areas and Riemann sums (M 11 November)
27. The definite integral (W 13 November)
28. The Fundamental theorem (F 15 November)

29. Evaluating definite integrals (M 18 November)
30. Substitution I (W 20 November)
31. Substitution II (F 22 November)

32. Integration by parts (M 25 November)
(No class W 27 November)
(No class F 29 November)

33. Area by slicing (M 2 December)
34. Integration with density (W 4 December)

Miscellaneous items

Class worksheets

These are listed by Tuesday/Thursday dates, according to when I used them in class. This list is incomplete, since I no longer have copies of many of the earlier worksheets.