Section(s) | ||||

1. | Riemann Sums | |||

a. | Examples | 5.4, 5.5 | ||

b. | Sigma Notation | 5.4 | ||

c. | Useful sums | 5.4 | ||

d. | Limits of sums | 5.5 | ||

2. | The Definite
Integral | |||

a. | Definition and notation | 5.6, 5.5 | ||

b. | Interpretations | 5.8 (sort of) | ||

c. | Sums, products and inequalities | 5.6 | ||

d. | Integrability | 5.6 | ||

3. | Antiderivatives | |||

a. | Definition and notation | 5.2 | ||

b. | Uniqueness | 5.2 | ||

c. | The Fundamental Theorem of Calculus | 5.7 | ||

d. | The indefinite integral | 5.2 | ||

4. | Integration Rules | |||

a. | Power, sum, product, quotient rules | 5.2 | ||

b. | Trigonometric rules | 5.2 | ||

c. | Integration by substitution | 5.3, 5.8 | ||

5. | Applications of Integration | |||

a. | Linear motion | 6.6 | ||

b. | Area under a curve, signed area | 5.5, 6.1 | ||

c. | Area between two curves | 6.1 | ||

d. | Volumes of revolution | 6.2, 6.3 | ||

e. | The Second Fundamental Theorem | 5.9 | ||

6. | Logs and Exponents | |||

a. | Antiderivative of 1/x | 7.5 | ||

b. | Properties of ln(x) | 7.5, 7.1, 7.2, 7.3 | ||

c. | Logarithmic differentiation | 7.2 | ||

d. | Function inverses | 7.4 | ||

e. | The exponential function | 7.5, 7.2 | ||

f. | Properties of e^{x} | 7.5, 7.1, 7.2, 7.3 | ||

g. | Log_{a} and a^{x} | 7.1, 7.5 | ||

h. | Graphs of exponential and log functions | 7.3 | ||

i. | Exponential growth | 7.7 | ||

7. | Inverse Trigonometric Functions | |||

a. | Graphs, domains, ranges | 8.1 | ||

b. | Triangle computations | 8.1 | ||

c. | Derivatives | 8.2 | ||

8. | More Integration Rules | |||

a. | Integrals resulting in inverse trig. functions | 8.2 | ||

b. | Integration by parts | 9.2 | ||

c. | Integrals of sin^{2}(x) and cos^{2}(x) | 9.3 | ||

9. | Improper Integrals | |||

a. | Convergence and divergence | 10.1 | ||

b. | Integrals over an infinite region | 10.1 | ||

c. | Integrals over an open interval | 10.1 | ||

10. | L'Hôpital's rule | |||

a. | Procedure | 10.2 | ||

b. | Iterated procedure | 10.2 | ||

c. | Other indeterminate forms | 10.3 |

See the course calendar for details concerning exams and quizzes.

Comments to: dpvc@union.edu

Created: Mar 24 1998 --- Last modified: Jun 1, 1998 10:27:48 AM