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.

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?

- 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

- 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

- 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

- Section 2.4 exercise(s): 5, 7, 17, 31

3:

### Monday #### Indeterminate forms - Factoring - Multiply by conjugate

- 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)

- Section 2.6 exercise(s): 5, 9, 17
### Thurs/Fri #### Limits at infinity - multiply by "one"

- 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)

- 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

- n/a
### Thurs/Fri #### Formal definition of a limit (continued) - finish Graphing calculator game - algebraic examples

- 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

- Section 2.9 exercise(s): 5 - Section 3.1 exercise(s): 1, 3, 9, 13, 15
### Tuesday #### Definition of a derivative - tangent lines

- Section 3.1 exercise(s): 21
### Wednesday #### Review - Clean out folders - review topics
### 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

- Section 3.2 exercise(s): 1, 7, 9, 11, 13, 15
### Tuesday #### Derivative as a function - review derivative rules: constants, power rule, coefficients, ex, ln(x), sum & difference - derivative intuition: Desmos, GeoGebra - relationship to continuity

- Section 3.2 exercise(s): 5, 17, 19, 32, 33, 35, 29, 43
### Wednesday #### Product and quotient rules - definitions & practice

- Section 3.3 exercise(s): 3, 7, 11, 19, 33, 37
### Thurs/Fri #### Higher derivatives - notation

- 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

- Section 3.4 exercise(s): 21, 27

7:

### Monday #### Rates of change - continue activity (Desmos) - other rates of change

- 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)

- 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

- 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

- Section 3.8 exercise(s): 1, 9, 15, 21, 23, 53

8:

### Monday #### Implicit differentiation (continued) - inverse trig functions - implicit differentiation with higher orders

- 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

- Section 3.9 exercise(s): 1, 3, 5, 11, 15, 17
### Thurs/Fri #### Related rates - falling ladder (Geogebra) - group exercises

- Section 3.10 exercise(s): 1, 3, 5, 7 - read relating those rates

9:

### Monday #### Related rates (continued) - group exercises

- Section 3.10 exercise(s): 9, 13, 15, 17
### Tuesday #### Linearization - locally linear using Desmos - review tangent lines - differentials

- Section 4.1 exercise(s): 21, 25, 27, 33, 57, 59, 61
### Wednesday #### Review - Clean out folders - review topics
### 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

- Section 4.2 exercise(s): 1, 3, 5 - discover local extrema - extrema introduction
### Tuesday #### Extrema (continued) - concavity, 2nd derivative test

- 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)

- 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

- Section 4.5 exercise(s): 1, 9, 11, 15, 27

11:

### Monday #### Graph sketching - inflection points - sketching: domain, intercepts, f', f'', asymptotes, holes

- 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
### Wednesday Finish sketching #### Applied optimization - optimization problems

- Section 4.7 exercise(s): 1
### Thurs/Fri #### Applied optimization (continued) - optimization problems

- Section 4.7 exercise(s): 3, 5, 7, 13

12:

### Monday #### Sigma notation - review Σ notation - introduce induction

- 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)

- Section 5.1 exercise(s): 3
### Thurs/Fri #### Computing area (continued) - Riemann sums (Desmos)

- Section 5.1 exercise(s): 5, 11, 15, 17

13: Thanksgiving week,

### Monday #### Review - Clean out folders - review topics - review proof by induction
### 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

- Section 5.2 exercise(s): 11a
### Tuesday #### Definite integral - signed area (Desmos) - properties

- Section 5.2 exercise(s): 1, 3, 5, 7, 9, 11b, 13, 19, 61, 63
### Wednesday #### Indefinite integral - anti-derivatives - notation and examples

- 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?

- 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

- 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

- 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

- 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