# 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:

Wednesday

#### Introduction

• Assign groups
• Syllabus game
• WeBWorK student demonstration
• review integration rules
• Book exercises (ungraded): 5.3 - 17, 24, 47
• Book exercises (ungraded): 5.4 - 15, 23, 37, 43
Thursday

#### Review

• review substitution
• Book exercises (ungraded): 5.5 - 25
• Book exercises (ungraded): 5.6 - 1
• Book exercises (ungraded): 5.7 - 7, 12, 19, 21
Friday

#### Area between two curves

• find intersections, y-Axis

### 2:

Monday

#### volume with cross sections

• identify cross sectional area
• Book exercises (ungraded): 6.2 - 11, 13
Wednesday

#### density and average value

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

Group quiz

Friday

### 3:

Monday

Wednesday

#### shell method

• shells: y-axis
• Book exercises (ungraded): 6.4 - 7, 15
Thursday

Group quiz

Friday

### 4:

Monday

#### trigonometric integrals

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

#### trigonometric integrals

• finish trig substitutions
• Book exercises (ungraded): 7.2 - 11, 29

#### work and energy

• lifting layers
• Book exercises (ungraded): 6.5 - 1, 11
Thursday

Friday

#### Exam 1

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

### 5:

Monday

#### trigonometric substitution

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

#### trigonometric substitution

• sqrt(x^2 - a^2)
• Book exercises (ungraded): 7.3 - 9, 11

#### partial fractions

• specifics
• Book exercises (ungraded): 7.5 - 33
Thursday

Group quiz

Friday

#### partial fractions

• linear factors,
• Book exercises (ungraded): 7.5 - 5, 9, 15, 29, 37

### 6:

Monday

#### strategies for integration

• worksheet
• Book exercises (ungraded): 7.6 - 19, 29
Wednesday

review limits at infinity from Calculus I

#### improper integrals

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

Group quiz

Friday

#### numeric integration

• midpoint, trapezoid, Simpson's rule
• Book exercises (ungraded): 7.9 - 1, 13

### 7:

Monday

#### arc length

• arc length: relationship to distance, Desmos, WolframAlpha
• Book exercises (ungraded): 8.1 - 7, 11, 13, 15
Wednesday

#### surface area

• surface area: relationship to truncated cone
• Book exercises (ungraded): 8.1 - 35
Thursday

Group quiz

Friday

#### center of mass (centroid)

• moments in x and y, alternate formula
• Book exercises (ungraded): 8.1 - 1, 11

### 8:

Monday

#### center of mass (centroid)

• moments in x and y, alternate formula
• Book exercises (ungraded): 8.1 - 21, 23
Wednesday

#### probability

• specifics
• Book exercises (ungraded): 7.8 - 1
Thursday

Friday

### 9:

Monday

New groups and review exam

#### Taylor polynomials

• example
• Book exercises (ungraded): 8.4 - 1, 19
Wednesday

#### 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
Thursday

Group quiz

Friday

#### slope fields

• Newton's law of cooling
• slope field example
• start Euler's method: polynomials, e^x (via GeoGebra)
• Book exercises (ungraded): 9.2 - 7
• Book exercises (ungraded): 9.3 - 1

### 10:

Monday

#### Euler's method

• finish Euler's method: polynomials, e^x (via GeoGebra)
• Book exercises (ungraded): 9.3 - 17

#### first order linear differential equations

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

Thursday

Group quiz

Friday

#### Sequences

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

### 11:

Monday

Wednesday

#### Convergence of positive terms

• integral test, p-series
• Book exercises (ungraded): 10.3 - 1, 3, 9
Thursday

Group quiz

Friday

#### Convergence of positive terms

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

### 12:

Monday

#### Practice day

• series practice
• Book exercises (ungraded): Chapter 10.3 - 49, 51, 53, 55, 57

### 13:

Monday

Wednesday

#### ratio and root tests

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

Read "Determine which test to apply" (10.5)

Friday

#### Exam 3

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

### 14:

Monday

#### Power series

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

#### Taylor series

• representations
• Book exercises (ungraded): 10.7 - 1, 39
Wednesday

#### Taylor series

• finish
• Book exercises (ungraded): 10.7 - 1, 39

Return exam and discuss

Thursday

Group quiz

Friday

### 15:

Monday

student evals

Wednesday

#### review

Thursday

Group quiz

• comprehensive
• note sheet allowed (1 page, one-sided, handwritten)
Friday

### Final exam

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