This is a tentative schedule that may be changed based on the needs of the students, the needs of the instructor, or any unforeseen events that may occur during the semester.
1:
### Thurs/Fri
#### Introductions
- Assign groups
-
syllabus scavenger hunt
- WeBWorK check?
#### Rates of change: Average vs instantaneous
- Provide a story for the
example
- 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?
Practice activities (not graded)
- Try
WeBWorK Introduction, report issues to instructor
2:
### Monday
#### Labor Day – no class
### Tuesday
#### Limits
- secant lines vs tangent lines:
one-sided
-
slope of x^2 at (2,4) & limit notation
-
two-sided
- other examples:
1,
2,
3
- Theorem 1
Practice activities (not graded)
- Section 2.1 exercise(s): 5, 9
- Section 2.2 exercise(s): 1, 5, 6
(degrees: ~0.017; radians: 1), 35, 37
- optional reading, Zeno's Paradox
### Wednesday
#### Limit laws
- Introduce
WolframAlpha
-
Limit law activity
Practice activities (not graded)
- Section 2.3 exercise(s): 9, 19, 27, 29, 31
### Thurs/Fri
#### Continuity at a number
- Point/removable discontinuity, jump discontinuity
- Substitution method for limits
Practice activities (not graded)
- Section 2.4 exercise(s): 5, 7, 17, 31
3:
### Monday
#### Indeterminate forms
- Factoring
- Multiply by conjugate
Practice activities (not graded)
- Section 2.5 exercise(s): 1, 3, 15, 17, 49, 51
### Tuesday
#### Group quiz
- no notes
- approved calculators allowed
### Wednesday
#### Trigonometric limits
- Squeeze theorem (
Desmos)
Practice activities (not graded)
- Section 2.6 exercise(s): 5, 9, 17
### Thurs/Fri
#### Limits at infinity
- multiply by "one"
Practice activities (not graded)
- Section 2.7 exercise(s): 5, 7, 9, 11, 13, 15, 21, 26
(horizontal asymptote at y=0, which f(x) crosses multiple times), 29
4:
### Monday
#### Intermediate value theorem
- review continuous functions and basic laws
- existence of zeros; existence of sqrt(2)
Practice activities (not graded)
- Section 2.8 exercise(s): 1, 7, 13, 19
### Tuesday
#### Group quiz
- no notes
- approved calculators allowed
### Wednesday
#### Formal definition of a limit
- ε-δ definition
-
Graphing calculator game
Practice activities (not graded)
- n/a
### Thurs/Fri
#### Formal definition of a limit (continued)
- finish
Graphing calculator game
- algebraic examples
Practice activities (not graded)
- Section 2.9 exercise(s): 1
5:
### Monday
#### Formal definition of a limit (continued)
- absolute value notation
- graph example
#### Definition of a derivative
- recall instantaneous rate of change
- generalize slope of tangent lines
Practice activities (not graded)
- Section 2.9 exercise(s): 5
- Section 3.1 exercise(s): 1, 3, 9, 13, 15
### Tuesday
#### Definition of a derivative
- tangent lines
Practice activities (not graded)
- Section 3.1 exercise(s): 21
### Thurs/Fri
#### Exam
- approved calculators
- one page of notes (one-sided, handwritten)
6:
### Monday
Discuss exam and new groups
#### Derivative as a function
- d/dx notation
- start
derivative rules
Practice activities (not graded)
- Section 3.2 exercise(s): 1, 7, 9, 11, 13, 15
### Tuesday
#### Derivative as a function
- review
derivative rules: constants, power rule, coefficients, e
x, ln(x), sum & difference
- derivative intuition:
Desmos,
GeoGebra
- relationship to continuity
Practice activities (not graded)
- Section 3.2 exercise(s): 5, 17, 19, 32, 33, 35, 29, 43
### Wednesday
#### Product and quotient rules
- definitions &
practice
Practice activities (not graded)
- Section 3.3 exercise(s): 3, 7, 11, 19, 33, 37
### Thurs/Fri
#### Higher derivatives
- notation
Practice activities (not graded)
- Section 3.5 exercise(s): 5, 11, 13, 15, 17
#### Rates of change
-
Desmos
- f(x) is increasing when f'(x) > 0
- f(x) is decreasing when f'(x) < 0
- distance, velocity, acceleration, and speed
-
activity
Practice activities (not graded)
- Section 3.4 exercise(s): 21, 27
7:
### Monday
#### Rates of change
- continue
activity (
Desmos)
- other rates of change
Practice activities (not graded)
- Section 3.4 exercise(s): 1, 7,
#### Trigonometric functions
- graph intuition for sin(x) and cos(x)
- methods for computing tan(x), csc(x), sec(x), cot(x)
Practice activities (not graded)
- Section 3.6 exercise(s): 5, 7, 11, 17, 19
### Tuesday
#### Group quiz
- no notes
- approved calculators allowed
### Wednesday
#### Trigonometric functions
- finish methods for computing tan(x), csc(x), sec(x), cot(x)
#### Chain Rule
-
decomposing functions
Practice activities (not graded)
- Section 3.7 exercise(s): 1, 3, 5, 9, 19, 31, 35, 45, 57
### Thurs/Fri
#### Implicit differentiation
- hidden chain rule
-
Desmos examples
-
challenge problems
Practice activities (not graded)
- Section 3.8 exercise(s): 1, 9, 15, 21, 23, 53
8:
### Monday
#### Implicit differentiation (continued)
- inverse trig functions
- implicit differentiation with higher orders
Practice activities (not graded)
- Section 3.8 exercise(s): 31, 33
### Tuesday
#### Group quiz
- no notes
- approved calculators allowed
### Wednesday
#### Logarithmic and exponential functions
- review exponential and logarithmic rules
- limit definition of e (
Desmos)
- "prove" d/dx e^x = e^x and d/dx ln(x) = 1/x
-
comic
Practice activities (not graded)
- Section 3.9 exercise(s): 1, 3, 5, 11, 15, 17
9:
### Monday
#### Related rates (continued)
-
group exercises
Practice activities (not graded)
- Section 3.10 exercise(s): 9, 13, 15, 17
### Tuesday
#### Linearization
- locally linear using
Desmos
- review tangent lines
- differentials
Practice activities (not graded)
- Section 4.1 exercise(s): 21, 25, 27, 33, 57, 59, 61
### Thurs/Fri
#### Exam
- approved calculator
- one page of notes (one-sided, handwritten)
10:
### Monday
Discuss exam, new groups
#### Extrema
- vocabulary: global/absolute, local/relative (
Desmos)
- critical numbers (aka. critical points) when f'(x) = 0 or DNE
- global test
- 1st derivative (local) test
Practice activities (not graded)
- Section 4.2 exercise(s): 1, 3, 5
-
discover local extrema
-
extrema introduction
### Tuesday
#### Extrema (continued)
- concavity, 2nd derivative test
Practice activities (not graded)
- Section 4.2 exercise(s): 21, 22, 41
- Section 4.4 exercise(s): 3, 5, 13
### Wednesday
#### Mean value theorem
-
MVT demo (Desmos)
-
MVT practice
-
MVT checker (Desmos)
- Rolle's theorem (from 4.2)
Practice activities (not graded)
- Section 4.3 exercise(s): 1, 5
### Thurs/Fri
#### Mean value theorem (continued)
-
MVT application
-
MVT checker (Desmos)
- Rolle's theorem (from 4.2)
#### L'Hopital's rule
Practice activities (not graded)
- Section 4.5 exercise(s): 1, 9, 11, 15, 27
11:
### Monday
#### Graph sketching
- inflection points
-
sketching: domain, intercepts, f', f'', asymptotes, holes
Practice activities (not graded)
- Section 4.6 exercise(s): 1, 7, 12
(f'=0 has no solutions; f''=0 has one solution at x=1, where f'' changes signs), 15
### Tuesday
#### Group quiz
- no notes
- approved calculators allowed
### Thurs/Fri
#### Applied optimization (continued)
-
optimization problems
Practice activities (not graded)
- Section 4.7 exercise(s): 3, 5, 7, 13
12:
### Monday
#### Sigma notation
- review Σ notation
- introduce
induction
Practice activities (not graded)
- Section 5.1 exercise(s): 23, 25, 29
- try
induction problems
- read Appendix C theorem 1
- try Appendix C exercise(s): 3
### Tuesday
#### Group quiz
- no notes
- approved calculators allowed
### Wednesday
Finish
sum of squares
#### Computing area
- geometric areas
- areas using rectangles (
Desmos)
Practice activities (not graded)
- Section 5.1 exercise(s): 3
### Thurs/Fri
#### Computing area (continued)
- Riemann sums (
Desmos)
Practice activities (not graded)
- Section 5.1 exercise(s): 5, 11, 15, 17
13: Thanksgiving week,
### Tuesday
#### Exam
- approved calculator
- one page of notes (one-sided, handwritten)
### Wednesday
#### Thanksgiving break – no class
### Thurs/Fri
#### Thanksgiving break – no class
14:
### Monday
Discuss exams and new groups
#### Definite integral
- infinite Riemann sums (
Desmos)
- integral notation
Practice activities (not graded)
- Section 5.2 exercise(s): 11a
### Tuesday
#### Definite integral
- signed area (
Desmos)
- properties
Practice activities (not graded)
- Section 5.2 exercise(s): 1, 3, 5, 7, 9, 11b, 13, 19, 61, 63
### Wednesday
#### Indefinite integral
- anti-derivatives
- notation and examples
Practice activities (not graded)
- Section 5.3 exercise(s): 1, 3, 5, 7, 11, 13, 23, 25, 63
### Thurs/Fri
#### Fundamental theorem of calculus, part 1
- initial condition problems
- how are definite integrals and anti-derivatives related?
Practice activities (not graded)
- Section 5.4 exercise(s): 1, 5, 9, 13, 23, 33
15:
### Monday
#### Fundamental theorem of calculus, part 2
- derivative of an integral
- the return of hidden chain rules
Practice activities (not graded)
- Section 5.5 exercise(s): 5, 7, 21, 29, 33, 35
### Tuesday
#### Group quiz
- no notes
- approved calculators allowed
### Wednesday
#### Integration with substitution
- chain rules for antiderivatives
Practice activities (not graded)
- Section 5.7 exercise(s): 3, 5, 7, 29, 81, 89, 91, 95
### Thurs/Fri
#### Net change
- distance vs displacement
- fnInt(function, X, lower, upper)
- ask for
review topics
Practice activities (not graded)
- Section 5.6 exercise(s): 1, 5, 9
- sample final posted to
Canvas
16:
### Monday
student evaluations
#### Review
- sample final posted to
Canvas
- sample final problems: 43, 37, {2, 3, 4}, {7, 8, 9}, 38, 12, {19, 20, 21, 22}, {27, 30}, 11, 6
- extra: solve #42 with Riemann sums as \(n \to \infty \)
answer will be \(\frac{488}{3} \)
- extra: derivative of \( 2 \cdot 3^{5x} \)
answer will be \( 10 \cdot \ln(3) \cdot 3^{5x} \)
-
review topics
Practice activities (not graded)
- see "final review" in
WeBWorK
### Tuesday
#### Review
- sample final posted to
Canvas
-
review topics
Practice activities (not graded)
- see "final review" in
WeBWorK