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 unforeseen events that may occur during the semester.
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Week 1: Limit introduction
### Monday
Introductions
#. assign groups
#.
syllabus scavenger hunt
#. complete
Canvas introductions
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?
#. recommended for next class
- try [WeBWorK "background - review"](https://uweau.instructure.com/courses/640161/assignments/6913208), report issues to instructor
#.
### Wednesday
Due today
-
Canvas introductions
Limit introduction
#. secant lines vs tangent lines:
one-sided
#.
slope of \(x^2\) at (3, 9) & limit notation
#.!
two-sided
#. other examples:
\( \frac{1-x^2}{1-x} \),
\( 5 \),
\( x \),
\( \frac{1}{x} \),
\( \frac{1}{x^2} \) (
Desmos limit idea)
#. theorem 1
#. recommended for next class
- [WeBWorK: motivating calculus - the language of change](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: limits - rates of change](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 2.1 exercise(s): 5, 9
- Section 2.2 exercise(s): 1, 5, 6
(degrees: ~0.017; radians: 1), 35, 37
#.
### Thursday
Limit laws
#. limits computed with tables/
Desmos vs Theorem 1
#. recommended for next class
- [WeBWorK: introducing limits - graphical limits](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: limit laws](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 2.3 exercise(s): 9, 19, 27, 29, 31
#.
### Friday
Continuity at a number
#. infinite/jump discontinuity, point discontinuity,
#. substitution method for limits
#. removable discontinuities (
desmos)
#. recommended for next class
- [WeBWorK: continuity - identifying discontinuities](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: continuity - making piecewise function](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 2.4 exercise(s): 5, 7, 17, 31
#.
Week 2: Limit rules
### Monday
Indeterminate forms
#. factoring
#. multiply by conjugate
#. recommended for next class
- [WeBWorK: continuity - challenge](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: indeterminate forms](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 2.5 exercise(s): 1, 3, 15, 17, 49, 51
#.
### Wednesday
book or WeBWorK questions?
Trigonometric limits
#. squeeze theorem (
Desmos)
#. \( \lim_{x \to 0} \frac{\sin{x}}{x} \)
#. recommended for next class
- [WeBWorK: limits of trigonometric functions](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: limits - squeeze theorem](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: limits - rates of change - challenge](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 2.6 exercise(s): 5, 9, 17
#.
### Thursday
Due today
- prepare for quiz
Quiz
- no notes
- approved calculators allowed
### Friday
Review quiz
Webwork soft deadlines (85% after each exam)
Limits at infinity
#. intuition for \( \lim_{x \to \infty} \frac{1}{x} \)
#. factor/multiply by "one"
#. recommended for next class
- [WeBWorK: limits at infinity](https://uweau.instructure.com/courses/640161/assignments/6913208)
- 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
#.
Week 3: Formal definition of a limit
### Monday
Intermediate value theorem
#. review continuous functions and basic laws
#. existence of zeros; existence of \( \sqrt{2} \)
#. recommended for next class
- [WeBWorK: limits intermediate value theorem - training](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: limits intermediate value theorem - challenge](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 2.8 exercise(s): 1, 5, 19
#.
### Wednesday
any book or WeBWorK questions?
Formal definition of a limit
#.
Graphing calculator game (
Desmos)
#. \( \epsilon\text{-}\delta \) definition
#. recommended for next class
- [WeBWorK: limits epsilon delta definition - training](https://uweau.instructure.com/courses/640161/assignments/6913208)
#.
### Thursday
Due today
- Prepare for quiz
Quiz
- no notes
- approved calculators allowed
### Friday
Formal definition of a limit (continued)
#. review \( \epsilon\text{-}\delta \) definition
#. algebraic examples
#. absolute value notation
#. graph example
#. recommended for next class
- [WeBWorK: limits epsilon delta definition - training](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 2.9 exercise(s): 1, 5
#.
Week 4: Definition of a derivative
### Monday
Definition of a derivative
#. recall instantaneous rate of change
#. generalize slope of tangent lines (
Desmos)
#. recommended for next class
- [WeBWorK: derivatives limit definition](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.1 exercise(s): 1, 3, 9, 13, 15
#.
### Wednesday
Definition of a derivative (continued)
#. tangent lines (
Desmos)
#. recommended for next class
- [WeBWorK: derivatives limit definition](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.1 exercise(s): 21
#.
### Thursday
Review
#. clean out folders
#.
review topics
#. create note sheet
#. continue WeBWorK and/or book problems
### Friday
Due today
- (optional) note sheet
Exam
#. approved calculators
#. note sheet (1 page, 1-sided, handwritten)
Week 5: Derivative rules
### Monday
Discuss exam, quiz changes for this week, midterm feedback, and new groups
Derivative as a function
#. d/dx notation
#. discuss
derivative rules
#. recommended for next class
- [WeBWorK: derivatives rates and slopes](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.2 exercise(s): 1, 7, 9, 11, 13, 15
#.
### Wednesday
Note: I may have jury duty so the goal today will be the WeBWorK problems below.
Derivative as a function (continued)
#. review
derivative rules
#. recommended for next class
- [WeBWorK: derivatives power rule and basic rules](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: derivatives power rule and slopes - challenge](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.2 exercise(s): 5, 17, 19, 32, 33, 35, 29, 43
#.
any book or WeBWorK questions?
### Thursday
Due today
- Prepare for quiz
Quiz
- no notes
- approved calculators allowed
### Friday
Product and quotient rules
#. definitions
#. WeBWorK and/or
challenge problems
#. recommended for next class
- [WeBWorK: derivatives product rule](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: derivatives quotient rule](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.3 exercise(s): 3, 7, 11, 19, 33, 37
#.
Week 6: Derivative rules, continued
### Monday
Higher derivatives
#. notation
#. check
challenge problem #3
#. recommended for next class
- [WeBWorK: higher order derivatives](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.5 exercise(s): 5, 11, 13, 15, 17
#.
Derivative concepts
#. derivative intuition:
Desmos,
GeoGebra
#. \( f' \gt 0 \implies f \text{ increasing }\)
#. \( f' \lt 0 \implies f \text{ decreasing }\)
#.
Desmos
#. relationship to continuity, \( f'(x) \implies \text{ continuous, but continuous } \centernot\implies f'(x) \)
#.
### Wednesday
Rates of change
#. distance, velocity, acceleration, and speed (
Desmos)
#.
activity
#. other rates of change
#. recommended for next class
- [WeBWorK: derivatives applied as rates of change](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.4 exercise(s): 21, 27, 1, 7
#.
### Thursday
Due today
- Prepare for quiz
Quiz
- no notes
- approved calculators allowed
### Friday
Trigonometric derivatives
#. graph intuition for sin(x) and cos(x)
#. methods for computing tan(x), csc(x), sec(x), cot(x)
#. recommended for next class
- [WeBWorK: trigonometric functions](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.6 exercise(s): 5, 7, 11, 17, 19
#.
Week 7: Chain rule
### Monday
Study abroad information
Chain Rule
#.
decomposing functions
#. recommended for next class
- [WeBWorK: derivatives chain rule](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.7 exercise(s): 1, 3, 5, 9, 19, 31, 35, 45, 57
#.
### Wednesday
Chain Rule
#. complete activities from last class
#. if time, introduce implicit differentiation (or hidden chain rule)
-
\(y^2=x\)
#. practice derivatives ("easy" to "little harder")
### Thursday
Due today
- Prepare for quiz
- make note sheet (1 page, 1-sided, handwritten) for individual section
Quiz
- note sheet for individual section only
- approved calculators allowed
### Friday
Review
#. Discuss quiz results
#. WeBWorK
Spring break
Week 8: Implicit differentiation
### Monday
Implicit differentiation
#. hidden chain rule
#.
Desmos examples
#. inverse trig functions
#. implicit differentiation with higher orders
#. if time,
challenge problems
#. recommended for next class
- [WeBWorK: derivatives differentiation on implicit curves](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.8 exercise(s): 1, 9, 15, 21
#.
### Wednesday
Logarithmic and exponential functions
#. review exponential and logarithmic rules
#. limit definition of e (
Desmos)
#. show \(\frac{d}{dx} e^x = e^x\) and \(\frac{d}{dx} \ln(x) = \frac{1}{x}\)
#.
comic
#. recommended for next class
- [WeBWorK: derivatives of exponential functions](https://uweau.instructure.com/courses/640161/assignments/6913208)
- [WeBWorK: derivatives of logarithmic functions](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.9 exercise(s): 1, 3, 5, 11, 15, 17
#.
### Thursday
Due today
- Prepare for quiz
- make note sheet (1 page, 1-sided, handwritten) for individual section
Quiz
- note sheet for individual section only
- approved calculators allowed
### Friday
Related rates
#.
falling ladder (Geogebra)
#.
group exercises
#. recommended for next class
- read
relating those rates
- [WeBWorK: derivatives relateid rates](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.10 exercise(s): 1, 3, 5, 7
#.
Week 9: Applications
### Monday
Related rates
#.
falling ladder (Geogebra)
#.
group exercises
#. recommended for next class
- read
relating those rates
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 3.10 exercise(s): 9, 13, 15, 17
#.
### Wednesday
Linear approximations
#. review tangent lines
#. locally linear
#. linearization
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 4.1 exercise(s): 21, 25, 27, 33, 57, 59, 61
#.
### Friday
Due today
- create note sheet
Exam
#. approved calculators
#. note sheet (1 page, 1-sided, handwritten)
Week 10: Extrema
### Monday
Discuss exam, new groups
Extrema using slopes
#. vocabulary: global/absolute, local/relative (
Desmos)
#. critical numbers (aka. critical points) when f'(x) = 0 or DNE
#. candidate's test
#. 1st derivative (local) test
#. [Desmos examples](https://www.desmos.com/calculator/fgplzoq23x)
#. recommended for next class
-
discover local extrema (GeoGebra)
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 4.2 exercise(s): 1, 3, 5
#.
### Wednesday
Extrema using slopes (continued)
### Thursday
Due today
- Prepare for quiz
any book or WeBWorK questions?
Quiz
- no notes
- approved calculators allowed
### Friday
Local extrema using concavity
#. concavity, 2nd derivative test
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 4.2 exercise(s): 21, 22, 41
- Section 4.4 exercise(s): 3, 5, 13
#.
Week 11: Mean Value Theorem
### Monday
Mean value theorem
#.
MVT demo (Desmos)
#.
MVT practice
#.
MVT checker (Desmos)
#. Rolle's theorem (from 4.2)
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 4.3 exercise(s): 1, 5
#.
### Wednesday
L'Hopital's rule
#. indeterminate forms
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 4.5 exercise(s): 1, 9, 11, 15, 27
#.
### Thursday
Due today
- Prepare for quiz
any book or WeBWorK questions?
Quiz
- no notes
- approved calculators allowed
### Friday
Applied optimization
#.
optimization problems
#. recommended for next class
- Section 4.7 exercise(s): 1, 3, 5, 7, 13
#.
Week 12: Computing area
### Monday
Math retreat: No class!
### Wednesday
Computing area
#. review \(\Sigma\) notation
#. useful results:
\(\Sigma 1\),
\(\Sigma i\),
\(\Sigma i^2\),
\(\Sigma i^3\)
#. geometric areas
#. finite Riemann sums (
Desmos)
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 5.1 exercise(s): 3, 5, 11, 15, 17
#.
### Thursday
Due today
- Prepare for quiz
any book or WeBWorK questions?
Quiz
- no notes
- approved calculators allowed
### Friday
Definite integrals
#. infinite Riemann sums (
Desmos)
#. integral notation
#. signed area (
Desmos)
#. properties
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 5.2 exercise(s): 1, 3, 5, 7, 9, 11, 13, 19, 61, 63
#.
Week 13: Integrals
### Monday
Student evaluations
Indefinite integral
#. Riemann sum with general upper bound
#. anti-derivatives
#. notation and examples
#. initial condition problems
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 5.3 exercise(s): 1, 3, 5, 7, 11, 13, 23, 25, 63
#.
### Wednesday
any book or WeBWorK questions?
Fundamental theorem of calculus, part 1
#. how are definite integrals and anti-derivatives related?
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 5.4 exercise(s): 1, 5, 9, 13, 23, 33
#.
### Thursday
Due today
- Prepare for quiz
Note: I am in Green Lake for conference
Quiz
- no notes
- approved calculators allowed
### Friday
Fundamental theorem of calculus, part 2
#. derivative of an integral
#. the return of chain rule
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 5.5 exercise(s): 5, 7, 21, 29, 33, 35
#.
Week 14: Integration rules
### Monday
Integration with substitution
#. chain rules for antiderivatives
#. definite integration with substitution (
Desmos)
#. recommended for next class
- [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
- Section 5.7 exercise(s): 3, 5, 7, 29, 81, 89, 91, 95
#.
### Wednesday
Net change
#. distance vs displacement
#. fnInt(function, X, lower, upper) or
Wolfram|Alpha
#. recommended for next class
- Section 5.6 exercise(s): 1, 5, 9
#.
### Thursday
Due today
- Prepare for quiz
any book or WeBWorK questions?
Quiz
- no notes
- approved calculators allowed
### Friday
Review for final exam
#. clean out folders
#.
review topics
#. [WeBWorK](https://uweau.instructure.com/courses/640161/assignments/6913208)
#. recommended
sample final problems: 1, 6, 7, 8, 9, 10, 11, 12, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 30, 31, 33, 34, 35, 36, 37, 38, 40, 41, 43 [(answers)](https://uweau.instructure.com/courses/564051/files/55968049)
#.! extra: solve #42 with Riemann sums as \(n \to \infty \)
answer will be \(\frac{488}{3} \)
#.
graph sketching: domain, intercepts, f', f'', asymptotes, holes, inflection points
#. recommended for next class
- Section 4.6 exercise(s): 1, 7, 15
#.
Finals week