Lecture(s)

Sections

Comments/Topics

1

1.1 – 1.3

Cartesian plane, distance formula, midpoint formula, graphs, intercepts, circles, and lines (Review the definition of absolute value on page O-8).

1.5

1.4

Functions, composition of functions, and inverse.

1.5

1.5

Limits

1

3.6

Vertical asymptotes and finite limits; horizontal asymptotes and limits of infinity.

1

1.6

Continuity

2

2.1

Slope of the tangent line, definition of the derivative, differentiability and continuity.

1

8.1 – 8.3

Trigonometry review

0.5

2..2

Constant rule, power rule, constant multiple rule, sum and differences rules.

1

2.3

Average rate change, instantaneous rate of change, velocity, marginals in economics.

1

2.4

Product and quotient rules.

1

8.4

Derivatives or trig functions.

1

2.5

Chain rule, general power rule (Include relevant problems from section 8.4).

0.5

2.6

Higher order derivatives, acceleration.

1

2.7

Implicit differentiation (Include relevant problems from Section 8.4).

1.5

2.8

Related rates.

1

3.1

Increasing and decreasing functions, critical numbers.

1.5

3.2

Relative extrema, the first-derivative test, absolute extrema (Include relevant problems from section 8.4 and page 612).

1

3.3

Concavity, points of inflection, the second-derivative test.

2

3.4

Optimization problems (You may want to assign some problems from section 3.5).

2

3.7

Sketching graphs (You may want to assign some problems from section 3.6).

1

3.8

Differentials (Explain estimating function values using differentials).