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:

Monday

Introductions

Rates of change: Average vs. instantaneous

  • Provide a story for the example (forward/backward only; no hills!)
  • 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?
  • Book exercises (ungraded): 2.1 - 4
Tuesday

Read WeBWorK FAQ

Try WeBWorK 0, report issues to instructor

Limits

Wednesday

Limit laws

Friday

Continuity and substitution

  • Continuous at a number
  • Removable discontinuity, jump discontinuity
  • Substitution method for limits
  • Book exercises (ungraded): 2.4 -

2:

Monday

Evaluating limits algebraically

  • Factoring
  • Multiply by conjugate
  • Book exercises (ungraded): 2.5 - 1, 3, 15, 17, 37, 49
Tuesday

Group quiz

Wednesday

Trigonometric limits

  • Squeeze theorem
  • Book exercises (ungraded): 2.6 - 5, 9, 17
Friday

Limits at infinity

  • Book exercises (ungraded): 2.7 - 3, 5, 9, 11, 13, 21, 23, 25

3:

Monday

Intermediate value theorem

  • review continuous functions and basic laws
  • Book exercises (ungraded): 2.8 - 1, 7, 13, 19
Tuesday

Group quiz

Wednesday

Formal definition of a limit

  • Graphing calculator game
  • ε-δ definition
  • Algebraic examples
  • abs notation
  • Book exercises (ungraded): 2.9 - 1, 9
Friday

Formal definition of a limit (continued)

  • Book exercises (ungraded): 2.9 - 4, 5

4:

Monday

Definition of a derivative

  • discuss non-example for formal definition
  • Book exercises (ungraded): 3.1 - 1, 3, 9, 13, 15
Tuesday

Definition of a derivative

  • tangent lines
  • Book exercises (ungraded): 3.1 - 21
Wednesday

Review

Friday

Exam

5:

Monday

New groups

  • return exam

Derivative as a function

  • derivative rules: constants, power rule, coefficients
  • Book exercises (ungraded): 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
  • Book exercises (ungraded): 3.2 - 1, 3, 5, 19, 32, 33, 35, 29, 43
Wednesday

Product and quotient rules

  • definitions & practice
  • Book exercises (ungraded): 3.3 - 3, 7, 11, 19, 33, 37
Friday

Higher derivatives

  • notation
  • Book exercises (ungraded): 3.5 - 5, 11, 13, 15, 17

Rates of change

  • geometry examples
  • distance, velocity (and speed), acceleration
  • activity
  • Book exercises (ungraded): 3.4 - 1, 7, 11, 21

6:

Monday

Rates of change

Trigonometric functions

  • Book exercises (ungraded): 3.6 - 5, 7, 11, 17, 19
Tuesday

Group quiz

Wednesday

Chain Rule

Friday

Implicit differentiation

7:

Monday

Implicit differentiation (continued)

  • inverse trig functions
  • implicit differentiation with higher orders
  • Book exercises (ungraded): 3.8 - 31, 33, 77
Tuesday

Group quiz

Wednesday

Review rates of change

  • f(x) is increasing when f'(x) > 0
  • f(x) is decreasing when f'(x) < 0

Logarithmic and exponential functions

  • Book exercises (ungraded): 3.9 - 1, 3, 5, 11, 17
Friday

Related rates

8:

Monday

Related rates (continued)

Tuesday

Linear approximation

  • Book exercises (ungraded): 4.1 - 13, 45, 47, 55, 57
Wednesday

Review

Friday

Exam

Spring break:

9:

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
  • Book exercises (ungraded): 4.2 - 1, 3, 5
Tuesday

Extrema

  • 2nd derivative test, concavity, inflection points
  • Book exercises (ungraded): 4.2 - 21, 22, 41
  • Book exercises (ungraded): 4.4 - 3, 5, 13
Wednesday

Mean value theorem

Friday

L'Hopital's rule

  • Book exercises (ungraded): 4.5 - 1, 9, 11, 15, 27

10:

Monday

Graph sketching

  • sketching: domain, intercepts, f', f'', asymptotes, holes
  • Book exercises (ungraded): 4.6 - 1, 7, 12, 15
Tuesday

Group quiz

Wednesday

Applied optimization

Friday

Applied optimization (continued)

11:

Monday

Proof by induction

Tuesday

Group quiz

Wednesday

Proof by induction

Friday

Computing area

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

12:

Monday

Definite integral

  • notation and properties
  • signed area
  • Book exercises (ungraded): 5.2 - 1, 11, 13, 15, 17, 33
Tuesday

Indefinite integral

  • anti-derivatives
  • notation and properties
  • initial condition problems
  • Book exercises (ungraded): 5.3 - 1, 3, 5, 7, 11, 13, 23, 25, 63
Wednesday

Review

Friday

Exam

13:

Monday

Logistics

  • discuss exam
  • new groups
  • discuss grading scale

Fundamental theorem of calculus, part 1

  • Book exercises (ungraded): 5.4 - 1, 5, 9, 13, 23, 33
Tuesday

Fundamental theorem of calculus, part 2

  • Book exercises (ungraded): 5.5 - 7, 21, 29, 31
Wednesday

Integration with substitution

  • Book exercises (ungraded): 5.7 - 3, 5, 7, 29, 81, 89, 91, 95
Friday

student evaluations

Displacement vs distance

  • Book exercises (ungraded): 5.6 - 1, 5, 9

14:

Monday

No class (Math Retreat)

Tuesday

Group quiz

Wednesday

Miscellaneous

  • advanced L'Hopitals cases
  • sample final posted to D2L
Friday

No class (Wisconsin Mathematics Council annual meeting)

15:

Monday

Group quiz

  • based on sample final
  • 5x7 note card allowed (both sides, handwritten)
Tuesday

Review

Wednesday

Group quiz (double points)

  • based on sample final
  • 5x7 note card allowed (both sides, handwritten)
Friday

Review

  • topics
  • challenging problems on sample final: 7, 12, 16, 31, 35

Final exam

(University finals schedule)