Lecture(s)

Sections

Comments/Topics

1.5

4.1 – 4.3

Exponential functions and their derivatives.

Note: You may want to skip the “proof” on page 273 that the exponential function is its own derivative, and justify this after you show in section 4.5 how to differentiate y = ln x, using the def. of the derivative).

1

4.4

Logarithmic functions

1.5

4.5

Derivatives of logarithmic functions

Note: Show how to differentiate functions of the form

y = [f(x)] ^ [g(x)]

1

4.6

Exponential growth and decay

Note: notice that the proof on page 299 is incomplete.

1

5.1

Antiderivatives and indefinite integrals

1

5.2

The General Power Rule

Note: Use this section as a simple introduction to substitution, rather than emphasizing the general power rule itself.

0.5

8.5

Simple trig integrals

Note: Introduce the integration rules on page 588. Point out that the substitution u = x in example one is never needed.

1

5.3

Exponential and logarithmic integrals

1.5

5.4

Definite integrals and the Fundamental Theorem of Calculus

Note: Mention that a more standard approach to definite integrals is presented in Appendix A.

1

5.5

Area of a region

Note: Present some examples of regions bounded by graphs of functions of y, since these are not included in the examples.

1.5

5.7

Volumes of solids of revolution (disc/washer method).

Note: You may want to show how to find the volume when a region is revolved around a general vertical or horizontal line.

1

6.1

Integration by substitution

1.5

6.2

Integration by parts

Note: you may want to introduce tabular integration (vertical integration by parts).

1

8.5

Trigonometric integrals

Note: Introduce the integrals on page 592. Mention that there are two common ways to write the anti-derivative of the tangent function.

1

6.3

Partial fractions

Note: Make it clear when division is necessary.

1.5

6.6

Improper integrals

1

9.1

Discrete probability

Note: This section is meant to motivate the ideas in the next two sections.

1

9.2

Continuous random variables

1.5

9.3

Mean and median; variance and standard deviation; uniform, normal, and exponential probability density functions.

0.5

5.6

The midpoint rule

Note: Point out that any integrals cannot be evaluated using the Fundamental Theorem of Calculus.

1

6.5

The trapezoidal rule and Simpson’s rule.

Note: do not require memorization of the error formulas on page 431.

0.5

6.4

Integration tables and completing the square.

Note: Make it clear that the formulas on pages 417-419 do not have to be memorized.