18.014 - Calculus with Theory (Fall 2015)

Schedule

Note: The schedule is subject to change. Check back for changes and updates. The schedule for later weeks will be filled in at a future date.

Semester Timeline
Date Topic References
A. Sept 9 (W) set theory I 2.1-2.4
1. Sept 10 (R) axioms for the real numbers, I: field and order axioms I 3.1-3.4
2. Sept 11 (F) integers, induction, summation notation I 3.6, I 4.1-4.2, I 4.6
3. Sept 15 (T) axioms for the real numbers, II: least upper bounds I 3.7-3.11
4. Sept 17 (R) roots, decimals, and the triangle inequality I 3.13-3.15, I 4.8
5. Sept 18 (F) functions, area axioms 1.2-1.10
6. Sept 22 (T) definition of the integral 1.12-1.17
7. Sept 24 (R) basic properties of the integral 1.18-1.21, 1.24, 1.27
8. Sept 25 (F) computing integrals 1.22-1.23, 1.25, 2.2-2.3
9. Sept 29 (T) indefinite integrals, introduction to continuity 2.18, 3.1
10. Oct 1 (R) limits and continuous functions 3.2-3.5, supplementary notes
11. Oct 2 (F) EXAM 1 (covers lectures 1-9)
12. Oct 6 (T) the intermediate value theorem 3.9-3.10
13. Oct 8 (R) composite and inverse functions 3.7, 3.12-3.13
14. Oct 9 (F) compactness properties of continuity 3.16-3.17
B. Oct 13 (T) integrability of continuous functions 3.18
15. Oct 15 (R) definition of the derivative 4.3-4.4
16. Oct 16 (F) properties of the derivative 4.5, 4.10-4.11
17. Oct 20 (T) the mean-value theorem 4.13-4.14
18. Oct 22 (R) more on extrema 4.16-4.17
19. Oct 23 (F) the fundamental theorem of calculus 5.1, 5.3
20. Oct 27 (T) logs and exps 6.2-6.7, 6.12-6.15
21. Oct 29 (R) trigonometric functions supplementary notes, 6.20-6.21
22. Oct 30 (F) EXAM 2 (covers lectures 10-19)
23. Nov 3 (T) integration by substitution and by parts 5.7, 5.9
24. Nov 5 (R) integrals of rational functions 6.23-6.24
25. Nov 6 (F) Taylor's formula 7.5-7.6
26. Nov 10 (T) more on Taylor's formula 7.2-7.3, 7.7, 7.9
27. Nov 12 (R) indeterminate forms 7.10
28. Nov 13 (F) L'Hopital's rule 7.12
29. Nov 17 (T) infinite limits 7.14-7.16
30. Nov 19 (R) infinite sequences 10.2-10.3
31. Nov 20 (F) EXAM 3 (covers lectures 20-29)
32. Nov 24 (T) infinite series 10.5-10.7
33. Dec 1 (T) convergence tests 10.11-10.13, 10.15
34. Dec 3 (R) conditional and absolute convergence 10.17-10.18, 10.21
35. Dec 4 (F) sequences of functions 11.1-11.4
36. Dec 8 (T) power series 11.5-11.6, 11.8
37. Dec 10 (R) Taylor series 11.9-11.11