# Calculus I

## Calendar

This is a tentative schedule that may be changed based on the needs of the students, the needs of the instructor, or any apocalyptic events that may occur during the semester.

### 1:

Monday

#### Rates of change: Average vs. instantaneous

• Provide a story for the example (forward/backward only; no hills!)
• What is the slope from (0, 0) to (30, 5)? What does this slope mean in context?
• What is the slope at (20, 3)? What does this slope mean in context?
• Book exercises (ungraded): 2.1 - 4

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Tuesday

Wednesday

Friday

#### Continuity and substitution

• Continuous at a number
• Removable discontinuity, jump discontinuity
• Substitution method for limits
• Book exercises (ungraded): 2.4 -

### 2:

Monday

#### Evaluating limits algebraically

• Factoring
• Multiply by conjugate
• Book exercises (ungraded): 2.5 - 1, 3, 15, 17, 37, 49
Tuesday

Group quiz

Wednesday

#### Trigonometric limits

• Squeeze theorem
• Book exercises (ungraded): 2.6 - 5, 9, 17
Friday

#### Limits at infinity

• Book exercises (ungraded): 2.7 - 3, 5, 9, 11, 13, 21, 23, 25

### 3:

Monday

#### Intermediate value theorem

• review continuous functions and basic laws
• Book exercises (ungraded): 2.8 - 1, 7, 13, 19
Tuesday

Group quiz

Wednesday

#### Formal definition of a limit

• Graphing calculator game
• ε-δ definition
• Algebraic examples
• abs notation
• Book exercises (ungraded): 2.9 - 1, 9
Friday

#### Formal definition of a limit (continued)

• Book exercises (ungraded): 2.9 - 4, 5

### 4:

Monday

#### Definition of a derivative

• discuss non-example for formal definition
• Book exercises (ungraded): 3.1 - 1, 3, 9, 13, 15
Tuesday

#### Definition of a derivative

• tangent lines
• Book exercises (ungraded): 3.1 - 21
Wednesday

Friday

### 5:

Monday

New groups

• return exam

#### Derivative as a function

• derivative rules: constants, power rule, coefficients
• Book exercises (ungraded): 3.2 - 7, 9, 11, 13
Tuesday

#### Derivative as a function

• notation
• derivative rules: e^x, ln(x), sum, difference
• relationship to continuity
• derivative intuition: GeoGebra, Desmos
• Book exercises (ungraded): 3.2 - 1, 3, 5, 19, 32, 33, 35, 29, 43
Wednesday

#### Product and quotient rules

• definitions & practice
• Book exercises (ungraded): 3.3 - 3, 7, 11, 19, 33, 37
Friday

#### Higher derivatives

• notation
• Book exercises (ungraded): 3.5 - 5, 11, 13, 15, 17

#### Rates of change

• geometry examples
• distance, velocity (and speed), acceleration
• activity
• Book exercises (ungraded): 3.4 - 1, 7, 11, 21

### 6:

Monday

#### Trigonometric functions

• Book exercises (ungraded): 3.6 - 5, 7, 11, 17, 19
Tuesday

Group quiz

Wednesday

Friday

### 7:

Monday

#### Implicit differentiation (continued)

• inverse trig functions
• implicit differentiation with higher orders
• Book exercises (ungraded): 3.8 - 31, 33, 77
Tuesday

Group quiz

Wednesday

Review rates of change

• f(x) is increasing when f'(x) > 0
• f(x) is decreasing when f'(x) < 0

#### Logarithmic and exponential functions

• Book exercises (ungraded): 3.9 - 1, 3, 5, 11, 17
Friday

### 8:

Monday

Tuesday

#### Linear approximation

• Book exercises (ungraded): 4.1 - 13, 45, 47, 55, 57
Wednesday

Friday

### 9:

Monday

#### Extrema

• vocabulary: global/absolute, local/relative
• discover local extrema and extra practice
• critical numbers (aka. critical points) when f'(x) = 0 or DNE
• global test
• 1st derivative (local) test
• Book exercises (ungraded): 4.2 - 1, 3, 5
Tuesday

#### Extrema

• 2nd derivative test, concavity, inflection points
• Book exercises (ungraded): 4.2 - 21, 22, 41
• Book exercises (ungraded): 4.4 - 3, 5, 13
Wednesday

Friday

#### L'Hopital's rule

• Book exercises (ungraded): 4.5 - 1, 9, 11, 15, 27

### 10:

Monday

#### Graph sketching

• sketching: domain, intercepts, f', f'', asymptotes, holes
• Book exercises (ungraded): 4.6 - 1, 7, 12, 15
Tuesday

Group quiz

Wednesday

Friday

### 11:

Monday

Tuesday

Group quiz

Wednesday

Friday

#### Computing area

• Book exercises (ungraded): 5.1 - 3, 15, 17, 23, 25, 29

### 12:

Monday

#### Definite integral

• notation and properties
• signed area
• Book exercises (ungraded): 5.2 - 1, 11, 13, 15, 17, 33
Tuesday

#### Indefinite integral

• anti-derivatives
• notation and properties
• initial condition problems
• Book exercises (ungraded): 5.3 - 1, 3, 5, 7, 11, 13, 23, 25, 63
Wednesday

Friday

### 13:

Monday

Logistics

• discuss exam
• new groups

#### Fundamental theorem of calculus, part 1

• Book exercises (ungraded): 5.4 - 1, 5, 9, 13, 23, 33
Tuesday

#### Fundamental theorem of calculus, part 2

• Book exercises (ungraded): 5.5 - 7, 21, 29, 31
Wednesday

#### Integration with substitution

• Book exercises (ungraded): 5.7 - 3, 5, 7, 29, 81, 89, 91, 95
Friday

student evaluations

#### Displacement vs distance

• Book exercises (ungraded): 5.6 - 1, 5, 9

### 14:

Monday

No class (Math Retreat)

Tuesday

Group quiz

Wednesday

#### Miscellaneous

• sample final posted to D2L
Friday

No class (Wisconsin Mathematics Council annual meeting)

### 15:

 Monday Group quiz based on sample final 5x7 note card allowed (both sides, handwritten) Tuesday Review topics fnInt()? Wednesday Group quiz (double points) based on sample final 5x7 note card allowed (both sides, handwritten) Friday Review topics challenging problems on sample final: 7, 12, 16, 31, 35