Syllabus

for MTH 251.01: Calculus III

Instructor:

Anita Johnston

Office and Office Hours:

JCC Main Campus - McDivitt 238 (Monday  9:00 - 12:00)
Potter Center Student Center 210HH (Tuesday & Wednesday 9:00 - 12:00)  
Other times by appointment

Phone and e-mail:

517.796.8504,  anita_johnston@jccmi.edu

 

 

Course Objectives

Students will demonstrate an understanding of:
aThree dimensional analytic geometry.  

a The calculus of vector-valued functions.

aThe calculus of multivariable functions.

a Vector analysis.

aSelected topics from linear algebra.

aCurrent technology relevant to the course material.  

The Board of Trustees has determined that all JCC graduates should develop or enhance certain essential skills while enrolled in the college. Several of these Associate Degree Outcomes (see below) are addressed in this class:

ADO 2. The ability to comprehend and use information including written and oral forms
ADO 3. Computational skills and understanding appropriate to the program of study
ADO 4. Critical thinking and problem-solving
ADO 7. Facility in the use of computers and other technologies appropriate to the program of study

Course Topics and Assigned Homework (AH)

To help you learn is recommended that you read the textbook, work through the examples, and do every other odd problem in the exercises at the end of each section.

 

TIMELINE IS SUBJECT TO CHANGE

NOTE:  Assigned Homework is INCOMPLETE:  Problems will be added to each assignment

Assigned Homework - 250 points: 50 lessons @ 5 apiece
Homework due next class period after assignment

 

Day

Section(s)

Topic

Jan 13

13.1,13.2

Three Dimensional Coordinates; Vectors

(AH) Sec 13.1: 8, 13, 15; Sec 13.2: 18, 25, 35

Jan 14

13.3

Dot and cross product

(AH) Sec 13.3: 5, 8, 18, 27, 34, 41, 52; Sec 13.1: 18; Sec 13.2: 34

Jan 15

13.4

Cross product
Sec 13.4: 5, 16, 27

Jan 16

13.5

Equations of Lines and Planes

(AH) Sec 13.5: 3, 8, 17, 18, 19, 20, 29, 33

Jan 20

NO CLASS

Inservice day for JCC employees

Jan 21

13.6

Graphing in 3-space: Cylinders

(AH) Sec 13.6: MAPLE plot 3-d

Identify surfaces 3, 6, 9, 12, 15, 18, 29, 32, 35, 37, 40

Jan 22

13.6

Graphing in 3-space: Quadratic surfaces

Jan 23

13.7

Cylindrical Coordinates

(AH) SEC 13.7: 3, 6, 31, 36, 38
NOTE: Jan 24 is last day to drop and not receive a “W”

Jan 27

13.7

Spherical Coordinates

(AH) SEC 13.7: 16, 21, 25, 30, 32, 34, 39, 45, 48, 51, 54
NOTE: Jan 27 is last day to drop and still get 100% tuition refund

Jan 28

14.1

Vector Functions and Space Curves

(AH) SEC 14.1: 1, 4, 13, 16, 21, 23, 26

Jan 29

14.2

Derivatives and Integrals of Vector Functions

(AH) SEC 14.2: 4, 7, 8, 10, 13, 19, 24, 33

Jan 30

14.3

Arc Length and Curvature

(AH) SEC 14.3: 1, 3, 7, 8, 12, 13, 16, 32

Feb 3

14.4

Motion in 3-space: Velocity and Acceleration

(AH) SEC 14.4: 2, 4, 6, 11, 15, 17, 29

Feb 4

Review

 

Feb 5

Review

 

Feb 6

EXAM 1

Chapters 13 and 14

Feb 10

15.1

Functions of Several Variables
(AH) Sec 15.1   2, 5, 6, 14, 18, 30, 32, 40, 51-56

Feb 11

 

PROJECT SUCCESS DAY

Feb 12

15.2

Limits and Continuity
AH) Sec 15.2   4, 6, 12, 15, 24, 31, 37

Feb 13

15.3

Partial Derivatives
(AH) Sec 15.3   4, 5, 6, 12, 20, 28, 35, 40, 50, 58, 64

Feb 17

15.4

Tangent Planes and Linear Approximations
AH) Sec 15.4   2, 6, 14, 17, 26, 30

Feb 18

15.5

The Chain Rule
AH) Sec 15.5  2, 6, 7, 10, 14, 21, 26, 34, 37

Feb 19

15.6

Directional Derivatives and Gradient
AH) Sec 15.6  2, 4, 9, 10, 14, 16, 23, 24, 34, 38, 42

Feb 20

15.7

Maximum and Minimum
(AH) Sec 15.7  2, 6, 11, 16, 28, 31, 50

Feb 24

15.8

LaGrange Multipliers
AH) Sec 15.8  4, 8, 10, 18

Feb 25

Review

 

Feb 26

EXAM 2

Chapter 15

Feb 27

16.1

Double Integrals over Rectangles
(AH) Sec 16.1  8, 12

Mar 3-9

Spring Break

 

Mar 10

16.2

Iterated Integrals
(AH) Sec 16.2  4, 8, 16, 23, 26

Mar 11

16.3

Double Integrals over General Regions
(AH) Sec 16.3  4, 12, 16, 19, 26, 35, 40

Mar 12

16.4

Double Integrals in Polar Coordinates
(AH) Sec 16.4  8, 11, 15, 20, 24, 29

Mar 13

16.5

Applications of Double Integrals
(AH) Sec 16.5  5, 9, 11, 17

Mar 17

16.6

Surface Area
(AH) Sec 16.6  2, 6, 10, 21

Mar 18

16.7

Triple integrals
(AH) Sec 16.7  4, 10, 15, 18, 29, 35

Mar 19

16.8

Triple Integrals in Cylindrical and Spherical Coordinates
(AH) Sec 16.8  3, 10, 13, 19, 22, 26

Mar 20

16.9

Change of Variables in Multiple Integrals
(AH) Sec 16.9  3, 6, 8, 11, 13, 20

Mar 24

Review

 

Mar 25

EXAM 3

Chapter 16

Mar 26

17.1

Vector Fields
(AH) Sec 17.1  4, 22

Mar 27

17.2

Line Integrals
(AH) Sec 17.2  2, 6, 10, 14, 20, 22, 38

Mar 30-Apr 6

County Break

 

Apr 7

17.3

Fundamental Theorem for Line Integrals
(AH) Sec 17.3  5, 6, 8, 13, 16, 18, 20, 22

Apr 8

17.4

Green’s Theorem
(AH) Sec 17.4  4, 8, 10, 14, 16, 20

Apr 9

17.5

Curl and Divergence
(AH) Sec 17.5  3, 7, 13, 15, 16

Apr 10

17.6

Parametric Surfaces and their Areas
(AH) Sec 17.6  1, 4, 12, 14, 17, 21, 24, 30, 32, 34, 36, 40

Apr 14

17.7

Surface Integrals
(AH) Sec 17.7  5, 7, 10, 16, 19, 22, 23

Apr 15

17.8

Stokes’ Theorem
AH) Sec 17.8  2, 4, 8, 13...find both sides if Stokes' Theorem and show they are equal

Apr 16

17.9

Divergence Theorem
(AH) Sec 17.9  5, 6, 8, 11, 16

Apr 17

17.10

Summary

Apr 21

Review

 

Apr 22

EXAM 4

Chapter 17

 

Linear Algebra

 

Apr 23

5.1 –5.2

Vector Spaces and Subspaces
AH) Sec 5.1  2, 4a, 4b, 5, 6; Sec 5.2  1c, 2d, 3b, 6b, 7a, 8f, 9b, 10d, 11, 12b, 19

Apr 24

5.3 – 5.4

Linear Combination of Vectors and Linear Dependence and Independence

AH) Sec 5.3, 1b, 1d, 2b, 2c, 3b, 4d, 5c, 6b, 7b, 10, 22b; AH) Sec 5.4 1b, 2d, 3b, 4d, 5b, 6b, 6c, 9

Apr 28

5.5 – 5.6

Basis and Dimensions and Rank of a Matrix

AH) Sec 5.5  1b, 2b, 3c, 3d, 5c, 5d, 6c, 6e, 6g, 9, 11, 14, 16b, 16d;
AH) Sec 5.6 1b, 2d, 2f, 3b, 4b, 6b, 7b, 9, 10a

Apr 29

5.7

Orthogonal Vectors and Projections in

AH) Sec 5.7  1c, 1e, 2c, 2d, 3b, 6b, 6d, 7b, 8b

Apr 30

6.1

Eigenvalues and Eigenvectors

AH) Sec 6.1  2, 6, 7, 11, 18, 30

May 1

6.3

Diagonalization

AH) Sec 6.3  1b, 2b, 3d, 4b, 5b

May 5

Review

 

May 6

EXAM 5

Linear Algebra

May 7

Review

 

May 8

Review

 

May 12

FINAL

 

May 13

FINAL

 

 

Course Requirements and Grading System – based on 1000 points

Exams - Five closed-book exams.  You may use one 8 ˝” x 11” sheet of paper for notes. If you must miss a test, contact me before the test is given in class to make arrangements for a make-up.  Once a test is returned, no make-up test will be given.

500 points
@ 100 points per exam

Final - A final exam with five pages of notes allowed (from exams) allowed.

150 points

Assigned Homework - Homework assignments as assigned throughout the course.  Homework is NOT intended to cover all the ideas with which you should be familiar.  Chapter Reviews and Exercises are excellent organizational tools for learning topics. 

250 points
50 assignments @ 5 each

Attendance - Attendance and participation in class is very important.  If you have special circumstances that make it difficult to meet attendance requirements, such as work or extended illness, please see me.  This will be recorded as beginning with 60 points.  You will lose one point each time you miss class.  You need to be in class for at least 40 minutes to be considered present.

60 points
@ 1 point per session

Projects

40 points

 

Total Points/ Numerical Grade

 

900+

850-899

800-849

750-799

700-749

650-699

600-649

<600

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.0

 

Late work Policy

aLate assignments will be assigned a 50% deduction the first class period it is late assuming you were present.  If you were absent all homework including assignments missed are due the class period you return.

a