# 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 ~number off
- 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)

- revolve around: x-axis (y=0), x-axis with washer, y=1, y=4
- Book exercises (ungraded):
**6.3**- 1, 15, 21, 29, 31

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

Wednesday

#### work and energy

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

Friday

Group quiz

### 4:

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

### 6:

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

Tuesday

#### arc length

- arc length: relationship to distance, Desmos visual, Desmos approximations, WolframAlpha
- Book exercises (ungraded):
**8.2**- 5, 11, 13, 15

Wednesday

#### surface area

- surface area (Desmos visual, Desmos truncated cone, Geogebra cone net)
- truncated cones (in train wheels): 1, 2, 3
- Book exercises (ungraded):
**8.2**- 37, 38 (10 pi sqrt(17))

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)

- practice worksheet
- Book exercises (ungraded):
**9.5**- 19

Wednesday

#### sequences

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

Friday

#### series

- partial sums: series vs sequence, Python version, geometric series
- Book exercises (ungraded):
**10.2**- 1a-c, 3, 11, 17, 23, 25, 29 (be careful where n starts!)

"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

- alternating series (divergent example)
- Book exercises (ungraded):
**10.4**- 1, 3, 5

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:

### Final exam

- approved graphing calculator
- one page of notes (one-sided, handwritten)
- Google search: calculus exams