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 unforeseen events that may occur during the semester.
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1:
Monday
introduction
- Assign groups ~number off
- syllabus scavenger hunt
- 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, triangles):
- 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)
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
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
- note sheet (1 page, 1-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
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
7:
No classes
8:
Spring break
9:
No classes
10:
Monday
probability
- probability density functions
- Book exercises (ungraded): 8.1 - 1
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
- interactive: Desmos, GeoGebra
- 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)
- note sheet (1 page, 1-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
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
- note sheet (1 page, 1-sided, handwritten)
- approved calculators
Final exam
- approved graphing calculator
- note sheet (1 page, 1-sided, handwritten)
- Google search: calculus exams
(University finals schedule)