Theorems of Differential Calculus; Riemann Sums:
- Read: end of chapter 4 (pp.201--207), section 5.1
- Goals: Recognize and understand the Extreme Value Theorem, Mean Value Theorem,
Constant Function Theorem, and the Racetrack Principle; be able to apply these theorems
to explain facts about abstract and particular functions; understand relationship between
distance traveled and area under velocity graph; use Riemann sums to approximate area.
- Required Problems: p.205: 1, 9. p.215: 2.
- Recommended Problems: p.205: 18. p.215: 1, 5, 9.
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Limits of Riemann Sums; Definite Integrals; Rules for Integrals:
- Read: sections 5.2, 5.4
- Goals: Understand how a limit of Riemann sums yields the exact area under a curve;
understand integral notation; interpret integrals as area; be able to estimate integrals;
use rules for integrals (sums, multiples, limits of integration).
- Required Problems: p.222: 13, 24. p.237: 14.
- Recommended Problems: p.222: 2, 10, 13, 15, 23, 25. p.237: 2, 15--19, 20, 21, 23, 24. p.240: 10.
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