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