Calculus I

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 #.
### Thursday Review #. clean out folders #. review topics
### 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

#### Final exam - approved calculator - ? 1 page notes (2-sided, handwritten) - Google search: calculus exams

(University finals schedule)