Text: Thomas' Calculus, Thomas, Weir, and Hass, Twelfth Edition, Pearson / Addison-Wesley, 2009, ISBN-13: 978-0321587992.
1. Real numbers and the real line (A.1: 1--4, 6--8, 11, 13--16, 19--22, 27). Functions and their graphs (1.1: 1--12, 14, 15, 17, 20, 22, 25, 29, 35, 37--39, 47, 48, 50--55, 72). Combining functions; shifting and scaling graphs (1.2: 1--5, 9, 17, 23, 25, 41, 51, 63, 67, 77, 85). Trigonometric functions (1.3: 4, 8, 13, 14, 18, 21, 29, 30, 32, 39, 41, 54).
2. Rates of change and tangents to curves (2.1: none). Limit of a function and limit laws (2.2: 2, 13, 15, 17, 19, 21, 33, 35, 37, 38, 40, 52, 60, 75). The precise definition of a limit (2.3: 26, 36, 37, 39, 44, 49, 54, 56). One-sided limits (2.4: 1, 5, 7, 11, 18--21, 25, 30, 31, 42, 46).
3. Continuity (2.5: 1--9, 13, 16--21, 29, 37, 41, 52, 59, 62, 65). Limits involving infinity; asymptotes of graphs (2.6: 1, 3, 5, 7, 10, 11, 13, 15, 18, 19, 21, 31, 35, 37, 39, 41, 43, 45, 47, 55, 67, 72, 77, 81, 83, 92, 101). Oblique asymptotes (general case).
4. Tangents and the derivative at a point (3.1: 7, 13, 23, 27, 33, 34, 36). The derivative as a function (3.2: 3, 9, 15, 21, 25, 27--30, 32, 37, 41, 42, 45, 47, 54, 58). Differentiation rules (3.3: 1, 3, 8, 11, 17, 19, 21, 23, 29, 33, 43, 47, 56, 65). The derivative as a rate of change (3.4: 1, 5, 7, 15, 22, 23).
5. Derivatives of trigonometric functions (3.5: 2, 3, 5, 15, 19, 33b, 35, 47, 49, 59, 65, 66). The chain rule (3.6: 3, 5, 8, 11, 13, 15, 17, 19, 21, 23, 26, 29, 31, 34, 36, 37, 61, 66, 71, 83, 88, 89, 94). Implicit differentiation (3.7: 3, 7, 21, 23, 35, 44, 47). Related rates (3.8: 1, 7, 11, 13, 23, 32, 34, 42).
6. Linearization and differentials (3.9: 3, 8, 17, 19, 21, 25, 26, 29, 33, 35, 37, 44, 48, 54ab, 55). Extreme values of functions (4.1: 1, 4, 5, 7, 9-14, 20, 23, 35, 51, 61, 63, 71, 76, 84). The mean value theorem (4.2: 5, 7--12, 17, 26, 28, 47, 64, 67). Monotonic functions and the first derivative test (4.3: 3, 17, 23, 26, 29, 31, 63ac, 70).
7. Inverse functions and their derivatives (7.1: 1, 3, 5, 12, 14, 15, 22, 31, 38, 53, 57, 58, 63). Inverse trigonometric functions (7.6: 1ab, 3ab, 11, 13, 15, 23, 100, 107, 116). L'Hôpital's rule I (basic indeterminate forms and the Cauchy mean value theorem) (7.5a: 4, 9, 11, 13--15, 17, 23, 25, 35, 47, 68, 75). Concavity and curve sketching (4.4: 1--3, 5, 7, 11, 23, 54, 88, 93, 94, 102, 112, 118).
8. Applied optimization (4.5: 3, 7, 15, 22, 24, 38, 61, 63). Newton's method (4.6: 5, 8, 21, 24). Antiderivatives (4.7: 5, 9, 15, 21, 31, 47, 57, 63, 67, 71, 83, 94). Area and estimating with finite sums (5.1: 4, 17, 23).
9. Sigma notation and limits of finite sums (5.2: 1, 3, 5, 8, 9, 12--15, 17, 19, 21, 25, 33, 39). The definite integral (5.3: 5, 9, 15, 18, 19, 23, 28, 41, 43, 45, 49, 53, 59, 71, 73--75, 81, 88, 97). The fundamental theorem of calculus (5.4: 1, 3, 5, 7, 9, 12, 14, 16, 18, 20, 21, 23, 25, 27, 29, 31, 34, 36--38, 40, 41, 47, 54, 55, 64, 65, 68).
10. Indefinite integrals and the substitution method (5.5: 2, 4, 6, 8, 9, 11, 13, 15, 17, 19, 21, 24, 25, 27, 29, 31, 34, 38, 40, 43, 45, 47, 49, 51, 55, 62, 63). Substitution and area between curves (5.6: 1, 3, 6, 7, 10, 12, 15, 17, 20, 24, 25, 29, 35, 43, 59, 63, 75, 79, 81--83, 86--88, 90a). Natural logarithms (7.2: 1, 4, 6, 8, 9, 12--15, 17, 20, 21, 23, 25--27, 36, 37, 39, 42, 43, 45, 47, 49, 51, 53, 54, 65, 67, 70, 81, 84). Exponential functions (7.3: 1, 5, 17, 23, 27, 29, 32, 34, 39, 42, 43, 47, 50, 51, 57, 71, 87, 91, 105, 109, 115, 119, 135a, 136; p.432, 123).
11. Exponential change and separable differential equations (7.4: 1, 3, 5, 7, 9, 11, 28, 39, 44). L'Hôpital's rule II (exponential indeterminate forms) (7.5b: 51, 53, 55, 57, 61, 71, 77, 80, 86, 88).
12. Hyperbolic functions (7.7: 1, 5, 11--13, 17, 21, 44, 45, 77, 86). Relative rates of growth (7.8: 2, 3, 6, 7, 9, 14, 18, 20). Integration by parts (8.1: 3, 5, 8, 10, 11, 13, 24--27, 30, 31, 33, 35, 37, 39, 41, 45, 47, 49, 51, 61, 65, 66, 68). Trigonometric integrals (8.2: 2, 3, 6, 8, 12, 14, 18, 19, 23, 25, 28, 29, 31, 33, 35, 37, 39, 42, 44, 45, 47, 49, 51, 62, 72).
13. Trigonometric substitutions (8.3: 1, 3, 5, 7, 9, 12, 13, 15--17, 19, 22, 23, 25, 29, 31, 33, 35, 37, 39, 40, 41, 43, 45, 48, 49, 57, 58). Integration of rational functions by partial fractions (8.4: 1, 3--7, 11, 15, 17, 21, 29, 41, 51, 59). Integral tables and computer algebra systems (8.5: 7, 28, 37, 44, 56, 67).
14. The substitution $z=\tan(x/2)$ (p.494: 41, 42, 45, 47). Numerical integration (8.6: 3, 9, 25, 28, 38). Improper integrals (8.7: 1--5, 7, 9, 11, 13, 16, 18, 19, 21--25, 27, 29, 32, 34, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 56, 58, 60, 61, 63, 65, 66, 73, 75b).