# 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

#### Introductions

- Assign groups
- Syllabus scavenger hunt
- Why calculus? (hardest part)
- WeBWorK student demonstration

#### 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

Tuesday

Read WeBWorK FAQ

Try WeBWorK 0, report issues to instructor

#### Limits

- secant lines vs tangent lines
- Notation & One-sided
- Numeric & graph examples: 1, 2, 3
- Zeno's paradox (or To Infinity and Beyond)
- Theorem 1
- Book exercises (ungraded):
**2.1**- 8, 9 - Book exercises (ungraded):
**2.2**- 1, 4, 5, 6, 17, 35, 40, 49

Wednesday

#### Limit laws

- Introduce Wolfram|Alpha
- Limit law activity
- Book exercises (ungraded):
**2.3**- 9, 27, 29, 31

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 ~verifying limit, not finding it
- 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

### 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

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

#### Rates of change

- distance vs displacement (activity)

#### Trigonometric functions

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

Tuesday

#### Group quiz

Wednesday

#### Chain Rule

- decomposing functions
- Book exercises (ungraded):
**3.7**- 1, 3, 5, 9, 19, 31, 35, 45, 57

Friday

#### Implicit differentiation

- practice problems
- Book exercises (ungraded):
**3.8**- 1, 9, 15, 21, 23, 53

### 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

#### Related rates

- examples: falling ladder
- extra practice
- relating those rates
- Book exercises (ungraded):
**3.10**- 1, 3, 5, 7

### 8:

Monday

#### Related rates (continued)

- extra practice: challenges
- Book exercises (ungraded):
**3.10**- 9, 13, 15, 17

Tuesday

#### Linear approximation

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

### Spring break:

### 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

#### Mean value theorem

- Rolle's theorem (from 4.2)
- MVT introduction (Desmos)
- MVT practice
- Book exercises (ungraded):
**4.3**- 1, 5

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

#### Applied optimization

- optimization problems
- Geogebra example
- Book exercises (ungraded):
**4.7**- 1

Friday

#### Applied optimization (continued)

- optimization problems
- Book exercises (ungraded):
**4.7**- 3, 5, 7

### 11:

Monday

#### Proof by induction

- review Σ notation
- induction introduction
- Appendix C theorem 1
- Book exercises (ungraded):
**Appendix C**- 1

Tuesday

#### Group quiz

Wednesday

#### Proof by induction

- continue induction introduction
- Appendix C theorem 1
- Book exercises (ungraded):
**Appendix C**- 3

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

### 13:

Monday

Logistics

- discuss exam
- new groups
- discuss grading scale

#### 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

Friday

#### No class (Wisconsin Mathematics Council annual meeting)

### 15:

Monday

Group quiz

- based on sample final
- 5x7 note card allowed (both sides, handwritten)

Wednesday

Group quiz (double points)

- based on sample final
- 5x7 note card allowed (both sides, handwritten)

### Final exam

- graphing calculator
- 5×7 note card (handwritten)
- Google search: calculus exams