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:

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)

- Read WeBWorK FAQ - 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: 5, 9 - Section 2.2: 1, 5, 6 (degrees: ~0.017; radians: 1), 35, 37 - optional reading, To Infinity and Beyond

Wednesday

#### Limit laws - Introduce Wolfram|Alpha - Limit law activity

Practice activities (not graded)

- Section 2.3: 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: 5, 7, 17, 31

3:

Monday

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

Practice activities (not graded)

- Section 2.5: 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: 5, 9, 17

Thurs/Fri

#### Limits at infinity - multiply by "one"

Practice activities (not graded)

- Section 2.7: 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

Practice activities (not graded)

- Section 2.8: 1, 7, 13, 19

Tuesday

#### Group quiz - no notes - approved calculators allowed

Wednesday

#### Formal definition of a limit - verify limit vs. computing limit value - Graphing calculator game - ε-δ definition - algebraic examples - absolute value notation

Practice activities (not graded)

- Section 2.9: 1, 9

Thurs/Fri

#### Formal definition of a limit (continued) - examples

Practice activities (not graded)

- Section 2.9: 4, 5

5:

Monday

#### Definition of a derivative - discuss non-example for formal definition

Practice activities (not graded)

- Section 3.1: 1, 3, 9, 13, 15

Tuesday

#### Definition of a derivative - tangent lines

Practice activities (not graded)

- Section 3.1: 21

Wednesday

#### Review - Clean out folders - Topics

Thurs/Fri

#### Exam - approved calculators - one page of notes (1 sided, handwritten)

6:

Monday

New groups - return exam #### Derivative as a function - derivative rules: constants, power rule, coefficients

Practice activities (not graded)

- Section 3.2: 7, 9, 11, 13

Tuesday

#### Derivative as a function - notation - derivative rules: e^x, ln(x), sum, difference - relationship to continuity - derivative intuition: GeoGebra, Desmos

Practice activities (not graded)

- Section 3.2: 1, 3, 5, 19, 32, 33, 35, 29, 43

Wednesday

#### Product and quotient rules - definitions & practice

Practice activities (not graded)

- Section 3.3: 3, 7, 11, 19, 33, 37

Thurs/Fri

#### Higher derivatives - notation

Practice activities (not graded)

- Section 3.5: 5, 11, 13, 15, 17 #### Rates of change - rates of change

- f(x) is increasing when f'(x) > 0 - f(x) is decreasing when f'(x) < 0 - geometry examples - distance, velocity (and speed), acceleration - activity

Practice activities (not graded)

- Section 3.4: 1, 7, 11, 21

7:

Monday

#### Rates of change - distance vs displacement (activity) #### Trigonometric functions

Practice activities (not graded)

- Section 3.6: 5, 7, 11, 17, 19

Tuesday

#### Group quiz - no notes - approved calculators allowed

Wednesday

#### Chain Rule - decomposing functions

Practice activities (not graded)

- Section 3.7: 1, 3, 5, 9, 19, 31, 35, 45, 57

Thurs/Fri

#### Implicit differentiation - practice problems

Practice activities (not graded)

- Section 3.8: 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: 31, 33, 77

Tuesday

#### Group quiz - no notes - approved calculators allowed

Wednesday

#### Logarithmic and exponential functions

Practice activities (not graded)

- Section 3.9: 1, 3, 5, 11, 17

Thurs/Fri

#### Related rates - examples: falling ladder - extra practice - relating those rates

Practice activities (not graded)

- Section 3.10: 1, 3, 5, 7

9:

Monday

#### Related rates (continued) - examples

Practice activities (not graded)

- Section 3.10: 9, 13, 15, 17

Tuesday

#### Linear approximation

Practice activities (not graded)

- Section 4.1: 13, 45, 47, 55, 57

Wednesday

#### Review - Clean out folders - Topics - Comic

Thurs/Fri

#### Exam - approved calculator - one page of notes (1 sided, handwritten)

10:

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

Practice activities (not graded)

- Section 4.2: 1, 3, 5

Tuesday

#### Extrema - 2nd derivative test, concavity, inflection points

Practice activities (not graded)

- Section 4.2: 21, 22, 41 - Section 4.4: 3, 5, 13

Wednesday

#### Mean value theorem - Rolle's theorem (from 4.2) - MVT introduction (Desmos) - MVT practice

Practice activities (not graded)

- Section 4.3: 1, 5

Thurs/Fri

#### L'Hopital's rule

Practice activities (not graded)

- Section 4.5: 1, 9, 11, 15, 27

11:

Monday

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

Practice activities (not graded)

- Section 4.6: 1, 7, 12, 15

Tuesday

#### Group quiz - no notes - approved calculators allowed

Wednesday

#### Applied optimization - optimization problems - Geogebra example

Practice activities (not graded)

- Section 4.7: 1

Thurs/Fri

#### Applied optimization (continued) - optimization problems

Practice activities (not graded)

- Section 4.7: 3, 5, 7

12:

Monday

#### Proof by induction - review Σ notation - induction introduction - Appendix C theorem 1

Practice activities (not graded)

- Section Appendix C: 1

Tuesday

#### Group quiz - no notes - approved calculators allowed

Wednesday

#### Proof by induction - continue induction introduction - Appendix C theorem 1

Practice activities (not graded)

- Section Appendix C: 3

Thurs/Fri

#### Computing area

Practice activities (not graded)

- Book exercises (ungraded): **5.1: 3, 15, 17, 23, 25, 29

13: (Thanksgiving week)

Monday

#### Review - Clean out folders - Topics

Tuesday

#### Exam - approved calculator - one page of notes (1 sided, handwritten)

Wednesday

#### Thanksgiving break – no class

Thurs/Fri

#### Thanksgiving break – no class

14:

Monday

Discuss exams / new groups #### Definite integral - notation and properties - signed area

Practice activities (not graded)

- Section 5.2: 1, 11, 13, 15, 17, 33

Tuesday

#### Indefinite integral - anti-derivatives - notation and properties - initial condition problems

Practice activities (not graded)

- Section 5.3: 1, 3, 5, 7, 11, 13, 23, 25, 63

Wednesday

#### Fundamental theorem of calculus, part 1

Practice activities (not graded)

- Section 5.4: 1, 5, 9, 13, 23, 33

Thurs/Fri

#### Fundamental theorem of calculus, part 2

Practice activities (not graded)

- Section 5.5: 7, 21, 29, 31

15:

Monday

student evaluations #### Integration with substitution

Practice activities (not graded)

- Section 5.7: 3, 5, 7, 29, 81, 89, 91, 95

Tuesday

#### Group quiz - no notes - approved calculators allowed ?

Wednesday

#### Net change

Practice activities (not graded)

- Section 5.6: 1, 5, 9

Thurs/Fri

#### Miscellaneous - advanced L'Hopitals cases - sample final posted to Canvas

16:

Monday

#### Review - topics - fnInt()?

Tuesday

#### Review - topics - challenging problems on sample final: 7, 12, 16, 31, 35

Final exam

- graphing calculator - 5×7 note card (handwritten) - Google search: calculus exams

(University finals schedule)