# 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