Calculus II

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

introduction

  • Assign groups
  • Syllabus game
  • review limits, derivatives, and integrals
  • Book exercises (ungraded): 5.2 - 18 (1.59), 27, 35, 37
  • Book exercises (ungraded): 5.3 - 17, 25, 47

Tuesday

review

  • review limits
  • Book exercises (ungraded): 5.4 - 5, 25, 37, 43
  • Book exercises (ungraded): 5.5 - 25

Wednesday

review

  • review integration with substitution
  • Book exercises (ungraded): 5.6 - 1
  • Book exercises (ungraded): 5.7 - 7, 12 ( 1/4 sin(x^4 + 4x) + C ), 19, 21

Friday

area between two curves

  • find intersections, y-Axis, challenge problem
  • Book exercises (ungraded): 6.1 - 1, 4 (128), 21

2:

Monday

volume with cross sections

  • identify cross sectional area using GeoGebra 3D (squares, semi-circles):
    • upper(x) = 2; lower(x) = 0; a = -2, b = 2; filling = 0
    • upper(x) = x + 2
    • upper(x) = -x^2 + 4
  • Exercise, 6.2.4
  • Book exercises (ungraded): 6.2 - 11, 13

Tuesday

density and average value

  • Book exercises (ungraded): 6.2 - 27, 43, 49

Wednesday

volumes of revolution (horizontal lines)

Friday

Group quiz

3:

Monday

volumes of revolution (vertical lines)

  • revolve around: y-axis (x=0), x=1, x=3, challenge
  • Book exercises (ungraded): 6.3 - 39, 47

Tuesday

shell method

  • shells: y-axis
  • Book exercises (ungraded): 6.4 - 7, 9

Wednesday

work and energy

  • lifting layers
  • Book exercises (ungraded): 6.5 - 1, 17

Friday

Group quiz

4:

Monday

integration by parts

Tuesday

trigonometric integrals

  • finish worksheet
  • start trig integrals
  • Book exercises (ungraded): 7.2 - 5

Wednesday

Review

  • (if needed) finish trig integrals
  • topics and samples
  • Book exercises (ungraded): 7.2 - 11, 29

Friday

Exam 1

  • one page of notes (one-sided, handwritten)
  • approved calculators

5:

Monday

Discuss exam and new groups

trigonometric substitution

  • sqrt(a^2 - x^2), sqrt(x^2 + a^2), sqrt(x^2 - a^2)
  • Book exercises (ungraded): 7.3 - 5

Tuesday

trigonometric substitution

  • challenge problems
  • Book exercises (ungraded): 7.3 - 9, 11

partial fractions

  • specifics
  • Book exercises (ungraded): 7.5 - 9 (A=-1/2, B=1/2), 15 (A=2, B=-1, C=-2), 29 (A=-1, B=1, C=-1, D=1)

Wednesday

partial fractions

  • linear factors
  • Book exercises (ungraded): 7.5 - 5 , 37

Friday

Group quiz

6:

Monday

strategies for integration

  • worksheet
  • Book exercises (ungraded): 7.6 - 15, 29

Tuesday

review limits at infinity from Calculus I

improper integrals

  • infinity and unbounded
  • Book exercises (ungraded): 7.7 - 5, 11, 15, 21, 61, 63

Wednesday

numeric integration

  • midpoint, trapezoid, Simpson's rule
  • Book exercises (ungraded): 7.8 - 1, 13

Friday

Group quiz

7:

No classes

8:

Spring break

9:

No classes

10:

Monday

probability

  • probability density functions
  • Book exercises (ungraded): 8.1 - 1

Tuesday

arc length

Wednesday

surface area

Friday

center of mass (centroid)

  • moments in x and y, alternate formula
  • Book exercises (ungraded): 8.4 - 1, 9

"Group" quiz posted (trigonometric identities)

11:

Monday

solving differential equations

  • first order, separable
  • y' = k(y - b) form
  • Book exercises (ungraded): 9.1 - 1, 15, 31
  • Book exercises (ungraded): 9.2 - 1, 3

Tuesday

slope fields

  • Newton's law of cooling
  • slope field example
  • Book exercises (ungraded): 9.2 - 7
  • Book exercises (ungraded): 9.3 - 1

Wednesday

Euler's method

  • Desmos: introduction
  • GeoGebra: polynomials, e^x
  • Book exercises (ungraded): 9.3 - 17 (y values: 1, 1.1, 1.22, 1.362, 1.5282, 1.72102)

Review

Friday

Exam 2 (online)

  • one page of notes (one-sided, handwritten)

12:

Monday

first order linear differential equations

  • Book exercises (ungraded): 9.5 - 1, 5, 13

Tuesday

first order linear differential equations (practice)

Wednesday

sequences

  • notation, limits (see Desmos), squeeze theorem
  • Book exercises (ungraded): 10.1 - 1, 3, 5, 9, 17, 23

Friday

series

"Group" quiz posted (trigonometric identities)

13:

Monday

convergence of positive terms

  • integral test, p-series
  • Book exercises (ungraded): 10.3 - 1 (1/24), 3, 9 (-1/5 ln(1/6))

Tuesday

convergence of positive terms

  • direct comparison, limit comparison (example comparisons)
  • Book exercises (ungraded): 10.3 - 15, 19, 21, 25, 39

Wednesday

absolute and conditional convergence

Friday

ratio and root tests

  • specifics
  • Book exercises (ungraded): 10.5 - 1, 5, 39, 43, 44 (converges by ratio test)

"Group" quiz posted (trigonometric identities)

14:

Monday

power series

  • ratio test for convergence
  • Book exercises (ungraded): 10.6 - 1, 3, 7, 9, 13, 35, 37

Tuesday

Taylor polynomial

  • example
  • Book exercises (ungraded): 10.7 - 1, 5

Taylor series

  • Book exercises (ungraded): 10.8 - 1, 3, 13, 31

Wednesday

Review

  • topics and samples
  • series practice: 1, 2
  • Book exercises (ungraded): Chapter 10.3 - 49, 51, 53, 55, 57

Friday

Exam 3

  • one page of notes (one-sided, handwritten)
  • approved calculators

15:

Monday

Review

Tuesday

Review

Wednesday

Review

"Group" quiz posted (trigonometric identities)

Friday

Review

Final exam

(University finals schedule)