# 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, 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

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

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

### 10:

Monday

#### probability

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

Tuesday

Wednesday

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)

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

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

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

Tuesday

Wednesday

#### Review

"Group" quiz posted (trigonometric identities)

Friday

### Final exam

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