Math 132 - Calculus II - Course Outline (Fall, 2017)

This is a tentative outline for the course and will be updated weekly.

Gateway Exam Pass List: http://macs.citadel.edu/bbaker/Gateway_Comp_F17_132.htm

 

Date

Topics

 

Aug 25

Review on integration: (5.3), (5.4)
(1) basic antidifferentiation formulas

     - Table of Indefinite Integral on Page 403
(2) the fundamental theorem of calculus: Part II

Lecture on Substitution: (5.5)

(3) substitution technique

Lecture Notes    

 

Worksheet 1

Homework 1:
 
Online: - due Sept 15
Section 5.5: 
Page 418: 
3, 5, 13, 17, 21, 23, 25, 28, 34, 35, 

38, 39, 40, 41, 44, 45, 53, 60, 62, 67

 

Turn in – due Aug 29
Page 418:  8, 14, 28 
Solutions
 

 

 

 

Aug 28

Lecture on Substitution: (5.5)

 

Homework 2:
 
Online: - due Sept 15
Section 5.5: 
Page 418:

3, 5, 13, 17, 21, 23, 25, 28, 34, 35,

38, 39, 40, 41, 44, 45, 53, 60, 62, 67

 

Turn in – due Aug 30
Page 418:  18, 34, 42, 44 
Solutions
 

Aug 29

Areas between curves (6.1)

Lecture Notes  

 

 

Homework 3:
 
Online: - due Sept 15
Section 6.1: 
Page 434:

1, 2, 3, 4, 9, 11, 12, 19, 21,

24, 27, 41

 

Turn in – due Sept 1
Page 434:  8, 12, 28
Solutions  

 

Aug 30

Quiz 1 on Section 5.5 Substitution
Solutions
 
Areas between curves (6.1)

Lecture Notes

 

Sept 1

 

Volumes (6.2)

(1) volumes: slicing method

(2) disc and washer 

Lecture Notes (get a copy here)

 

Homework 4:
 
Online: - due Sept 15
Section 6.2: - Page 446 
3, 5, 7, 9, 11, 13, 14, 15, 
23, 25, 28,
54, 55, 56, 57, 58 

 

Turn in – due Sept 5
Page 446: 8, 12, 14, 24, 28
For each problem, 
(1) sketch the region,
(2) sketch one cross-section,
(3) give the area of the cross-section in terms of x or y, and
(4) set up a definite integral that gives the volume.
Solutions  
 
 
Turn in – due Sept 15

Page 446: 56, 58

For each problem, 
(1) sketch the region of the base,
(2) sketch one cross-section,
(3) give the area of the cross-section in terms of x or y, and
(4) set up a definite integral that gives the volume.

Solutions

 

 

 

Sept 4

Quiz 2 on 5.5 Substitution

Solutions

 

Volumes (6.2)

(1) volumes: slicing method

(2) disc and washer 

Lecture Notes (get a copy here)

 

 

Sept 5

Volumes by Cylindrical Shells (6.3)

Lecture Notes (get a copy here )

Homework 5:
 
Online: - due Sept 18
Section 6.3: - Page 453 
2, 5, 7, 8, 15, 17, 19, 23, 25

 

Turn in – due Sept 15
Page 453: 6, 10
For each problem, 
(1) sketch the region,
(2) sketch one cross-section,
(3) give the area of the cross-section in terms of x or y, and
(4) set up a definite integral that gives the volume.
Solutions
 
Turn in – due Sept 18

Page 453: 14, 18

For each problem, 
(1) sketch the region of the base,
(2) sketch one cross-section,
(3) give the area of the cross-section in terms of x or y, and
(4) set up a definite integral that gives the volume.

Solutions

Sept 6

Quiz 3 on Section 6.1

Solutions

 

Volumes by Cylindrical Shells (6.3)

 

Sept 8-

13

Evacuation for Irma

 

Sept 15

Average Value of a Function (6.5)

Lecture Notes  (get a copy here)

Homework 6:
 
Online: - due Sept 22
Section 6.5: - Page 463 
4, 5, 6, 7, 8, 9, 11, 14, 16, 17

 

Turn in – due Sept 20
Page 463: 6, 10, 20

Solutions

 

 

 

Sept 18

Quiz 4 on Section 6.2

Solutions

 

Review for Hour Exam 1: Section 5.5, 6.1, 6.2, 6.3, 6.5

 

 

Sept 19

Quiz 5 on Section 6.3

Solutions

 

Integration by parts (7.1)

Lecture Notes  (get a copy here)

 

Sept 20

Integration by parts (7.1)

Homework 7:
 
Online: - due Sept 28
Section 7.1: - Page 476
1,3, 5 ,7,9,11,15,17,19,26,28,39 

 

Turn in – due Sept 26

Page 476: 4, 6, 20, 26

For each problem, specify first u, du, dv and v.

Solutions

 

 

Turn in – due Sept 27

Page 476: 12, 22, 32, 18

For each problem, specify first u, du, dv and v.

Solutions

 

Sept 22

Hour Exam 1: Section 5.5, 6.1, 6.2, 6.3, 6.5

Exam 1

 

Solutions

 

 

 

 

Sept 25

Integration by parts (7.1)

 

Sept 26

Trigonometric Techniques of Integration (7.2)

  (1) Integrals involving sinm(x)cosn(x)
  (2) Integrals involving tanm(x)secn(x)

Lecture Notes 

 

Homework 8:
 
Online: - due Oct 3
Section 7.2: - Page 484
1, 2, 3,7, 10, 11, 21,23, 25,27, 
29, 31, 41, 43 

 

Turn in – due Sept 29

Page 484: 2, 6, 10, 22

For each problem, specify first u, du

Solutions

 

 

Turn in – due Oct 3

Page 484 : 14. 18, 42, 28, 32 

For each problem, specify first u, du

Solutions

 

Sept 27

Trigonometric Techniques of Integration (7.2)

 

Sept 29

Quiz on Section 7.1

Solutions

 

Trigonometric Substitute (7.3)

Lecture Notes

Homework 9:
 
Online: - due Oct 10
Section 7.3: - Page 491
2, 3, 4, 9, 12, 13, 19, 21, 22, 37

 

Turn in – due Oct 4

Page 491: 4, 8, 12

For each problem, specify first the substitution for x.

Solutions

 

 

Turn in – due Oct 6

Page 491: 5, 22, 38 

For each problem, specify first the substitution for x.

Solutions

 

 

 

 

Oct 2

Trigonometric Substitute (7.3)

 

 

Oct 3

Trigonometric Substitute (7.3)

 

 

Oct 4

Integration of rational functions  (7.4)
(1) partial fractions decomposition
(2) integration of rational functions

Lecture Notes

Homework 10:
 
Online: - due Oct 12
Section 7.4: - Page 501
2, 4, 9, 12, 19, 23, 24, 26, 31, 32

 

Turn in – due Oct 9

Page 501: 12, 16

 

 

Turn in – due Oct 11

Page 501: 24, 28, 32

 

Oct 6

Quiz on Section 7.2

Solutions

 

Integration of rational functions  (7.4)

 

 

 

 

Oct 9

Integration of rational functions  (7.4)

 

Oct 10

Quiz on Section 7.3

Solutions

 

Indeterminate Forms (4.4)

Homework 11:
 
Online: - due Oct 17
Section 4.4: - Page 311
13, 19, 20, 25, 27, 31, 32, 33, 

 

Turn in – due Oct 9

Page 501: 12, 16

 

 

Turn in – due Oct 11

Page 501: 24, 28, 32

 

Oct 11

Integration of rational functions  (7.4)

 

 

Oct 13

 

Indeterminate Forms and L’Hospital

 

Lecture Notes 

Homework 12:
 
Online: - due Oct 20
Section 4.4: - Page 311
13, 19, 20, 25, 27, 31, 
32, 33, 41, 47, 51, 52, 56, 58, 
59, 63, 69

 

Turn in – due Oct 16

Page 311: 18, 22, 25 (show your work)

 

 

Turn in – due Oct 20

Page 311: 32, 40

 

 

Turn in – due Oct 24

Page 311 : 54, 56, 58, 64 

Solutions

 

 

 

 

Oct 16

Quiz on Section 7.4

Solutions

 

 

Review for Hour Exam 2:

Section 7.1-7.4, 4.4 (part 1, 0/0, inf/inf)

 

 

Oct 17

Hour Exam 2: Section 7.1-7.4, 4.4 (part 1)

Exam 2

 

Solutions

 

Oct 18

Leadership Day

 

Oct 20

Indeterminate Forms and L’Hospital

(0^0. 1^inf,  inf^0)

 

Improper Integrals (7.8)

 

Gateway Exam for Integration Techniques

 

Homework 13:
 
Online: - due Oct 30
Section 7.8: - Page 534
5, 6, 9, 13, 14, 15, 21, 23, 31,
32, 35

 

Turn in – due Oct 25

Page 534: 6, 14

 

 

Turn in – due Oct 27

Page 534: 22, 24, 28, 32

 

 

 

 

Oct 23

Improper Integrals (7.8)

Lecture Notes 

 

Oct 24

Improper Integrals (7.8)

 

Oct 25

Arc Length (8.1)

Lecture Notes 

Homework 14:
 
Online: - due Nov 3
Section 8.1: - Page 548
7, 9, 13, 19, 21

 

Turn in – due Oct 31

Page 548: 4, 14, 20

 

Oct 27

 

Arc Length (8.1)

 

Surface Area of a Region Obtained by Rotating a Curve about the x-axis and y-axis  (8.2)

Lecture Notes 

 

 

 

 

Oct 30

Quiz on Section 4.4

Solutions

 

 

Surface Area of a Region Obtained by Rotating a Curve about the x-axis and y-axis  (8.2)

Lecture Notes 

Homework 15:
 
Online: - due Nov 6
Section 8.2: - Page 555
5, 7, 8, 10, 13, 15, 27, 28

 

Turn in – due Nov 3

Page 555: 8, 14, 18, 28

Solutions

Oct 31

Surface Area of a Region Obtained by Rotating a Curve about the x-axis and y-axis  (8.2)

 

Nov 1

Quiz on 7.8

Solutions

 
Moments and Center of Mass (8.3)
(1) moments of the system about the y-axis and x-axis
(2) the centroid: the center of mass of a plate

Lecture Notes

Homework 16:
 
Online: - due Nov 8
Section 8.3: - Page 565
25, 27, 29, 31, 32

 

Turn in – due Nov 7

Page 565: 26, 28, 32

Nov 3

Moments and Center of Mass (8.3)
(1) moments of the system about the y-axis and x-axis
(2) the centroid: the center of mass of a plate

 

 

 

 

Nov 6

Review for Hour Exam 3: Sections 4.4, 7.8, 8.1-8.3

 

Sequences and series (11.1)

(i) definition of a sequence

(ii) limit of a sequence
(iii) convergence and divergence of a sequence

Lecture Notes

 

Nov 7

Hour Exam 3: Section 4.4, 7.8, 8.1-8.3

Formulas for Exam 3

 

Exam 3

 

Solutions

Homework 17:
 
Online: - due Nov 16
Section 11.1: - Page 704

5, 9, 15, 23, 29, 30, 33, 37, 38, 41,

42, 47, 49, 55

Turn in – due Nov 10

Page 704: 6, 10, 14, 16

 

Turn in – due 14

24, 30, 36, 48, 52, 56

Solutions

Nov 8

 

Sequences and series (11.1)

 

 

Nov 10

 

Sequences and series (11.1)

 

 

 

 

Nov 13

Series (11.2)

(1) infinite series
(2) partial sums of a series
(3) convergence of a series defined by the limit of the sequence of partial sums
(4) geometric series:
(5) the nth-term test for divergence
(6) properties of convergent series
(7) harmonic series
Lecture Notes

 

Summary on Sequence and Series

Homework 18:
 
Online: - due Nov 27
Section 11.2: - Page 715:

3, 15, 18, 19, 22, 23, 31, 37,

39, 41, 43, 44, 45, 52, 53, 57

 

Turn in – due Nov 16

Page 715: 12, 18, 22, 26, 44, 46

Solutions

Nov 14

Series (11.2)

 

Nov 15

Quiz on Section 11.1

Solutions

 

Section 11.3

Integral Test and Estimates of Sums

Lecture Notes

Homework 19:
 
Online: - due Nov 28
Section 11.3: - Page 725:

7, 8, 11, 14, 15, 17, 21, 25,

35, 37, 39

 

Turn in – due Nov 17

Page 725: 8, 14, 22, 26

Solutions

 

Turn in – due Nov 27

Page 725: 36, 38

Solutions

Nov 16

 

Noon 12: Section 11.3

 

 

Nov 17

Quiz on Section 11.2

Solutions

 

Section 11.4 Comparison and Limit Comparison

Tests

Lecture Notes

 

 

 

 

Nov 27

Section 11.4 Comparison and Limit Comparison

Tests

 

Section 11.5 Alternating Series

Lecture Notes

Homework 20:
 
Online: - due Dec 4
Section 11.4: - Page 731:

5, 7, 15, 17, 19, 20, 23, 28

 

Turn in – due Nov 29

Page 731: 8, 14, 26, 28

Solutions

Nov 28

 

Section 11.5 Alternating Series

 

 

Homework 21:
 
Online: - due Dec 5
Section 11.5: - Page 736:

4, 6, 7, 11, 13, 19, 23

 

Turn in – due Dec 1

Page 736: 8, 12, 22

Solutions

Nov 29

Quiz on Section 11.3

Solutions

 

Section 11.6 Absolutely Convergence and Ratio Test

Lecture Notes

Homework 22:
 
Online: - due Dec 6 
Section 11.6: - Page 742:

1, 2, 3, 4, 7, 8, 9, 19, 13, 18, 23

 

Turn in – due Dec 4

Page 742: 2, 4, 8, 14

Solutions

Dec 1

10am

Section 11.8 Power Series

Lecture Notes

 

5pm

Section 11.9-10 Power Series Representation

and Taylor Series

Lecture Notes

 

Power Series and Taylor Series formulas

 

Homework 23:
 
Online: - due Dec 7 
Section 11.8: - Page 751:

3, 4, 5, 6, 7, 14, 16, 17

 

Turn in – due Dec 5

Page 751: 4, 6, 12, 16

 

Homework 24:
 
Online: - due Dec 8 
Section 11.9: - Page 757:

3, 7, 8, 13, 15, 16, 17, 23, 25, 27

 

Turn in – due Dec 7

Page 757: 8, 16, 22, 32

 

Homework 25:
 
Online: - due Dec 8 
Section 11.10: - Page 771:

12, 14, 22, 23, 35, 39, 43,

45, 55

 

Turn in – due Dec 8

Page 771: 16, 40, 48, 54

 

 

 

Dec 4

Review for Hour Exam 4 – Section 11.1-11.6, 11.8

 

Dec 5

Hour Exam 4 – Sections 11.1-11.6, 11.8

Exam 4

 

Solutions

 

Dec 6

Review for Final Exam

 

 

 

 

Final Exam

Dec 8: 5:30pm-8:30pm

or

Dec 11: 1pm-4pm

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