Syllabus

Calculus III, Mathematics 2470                                       Office:  Newton Oakes 222

4 hours                                                                                  864-1809     

Fall 2009                                                                                egreen@ngcsu.edu

Dr. Green                                                                              Office Hours:       9:00 – 11:00  MWF,  1:15 – 2:15 TR,  4:30 – 5:30  MW

                                                                                                                                                (or by appointment)

 

Prerequisite:  Grade of C or above in MATH 2460 or approval of the department head.

 

Catalog Description: A continuation of Calculus II.  Topics include functions of several variables; partial differentiation; multiple integrals; vector algebra, lines, planes, and curves in three dimensions; and vector calculus.

 

Course Objectives:  After completion of the course the student will be able to:

·         Find partial derivatives of functions of several variables.

·         Use partial derivatives to find local maxima and local minima of functions of two variables.

·         Use the chain rule for differentiation to find derivatives of functions of several variables.

·         Obtain the gradient of a function of three variables, and use this gradient to find the direction in which the function changes most rapidly, and the rate of this most rapid change.

·         Evaluate multiple integrals involving rectangular and polar coordinates, and use these integrals for the purpose of finding areas and volumes.

·         Determine an appropriate coordinate system for simplification of a double or triple integral.

·         Perform the operations of vector addition, subtraction, and scalar multiplication in two and three dimensions and interpret geometrically.

·         Find the dot product of two vectors and interpret geometrically.

·         Find the cross product of two vectors and interpret geometrically.

·         Find the triple scalar product of three vectors and interpret geometrically.

·         Find the length of a space curve from one specified point to another specified point.

·         Evaluate the work done in carrying a particle from one point to another point in a given force field.

·         Determine whether the work is independent of the path taken between the two points.

·         Interpret and apply Green’s Theorem and Stokes’ Theorem to rewrite a surface integral as integral around the curve bounding the surface.

·         Interpret and apply the Divergence Theorem to rewrite a volume integral as an integral over the surface bounding the volume.

 

Methods of  Instruction:  The methods of instruction are determined by the instructor; however, the instructor is expected to use a variety of methods.  These methods may include, but are not limited to lecture; problem-solving sessions with informal assessment by the student or instructor; discussion; group projects; timely feedback from test, quiz, or project results (formative assessment); question and answer; computer or calculator based explorations; and student presentations.  Students will be encouraged to assess and monitor their own problem-solving process to determine when an error has been made or a new strategy should be used.

 

Metacognitive Model and Teacher Education Program Competencies:   

The NGCSU Secondary Mathematics Education Program prepares teachers to assume within the school community the roles of Decision-Maker, Facilitator, and Leader as identified in the metacognitive model.  Twelve Teacher Education Program competencies reflecting the model are aligned to a specific role.  Overlap into more than one role and mathematics course may occur.  Current research and professional standards identify these competencies as important for effective teaching (NBPTS and ASCD Framework). 

 

Decision-Maker

Facilitator

Leader

Assessment

Individual Differences

Ethical Perspectives

Planning

Subject Matter Knowledge

Reflection/Metacognition

Problem Solver

Communication

Professional Leadership

Methods, Materials, Resources

Classroom Management

Research & Evaluation

 

Evaluation Methods:   (See Calendar for Test Dates)

                Test average:  Average of 4 major tests and Question of the Week Total:  2/3 or 1/3

                2 Bonus Projects will be offered – these use Maple

                Final Exam 1/3 or 2/3       (2/3 if higher than test average)

 

Course Content:

1.  Functions of several variables. Partial differentiation with applications

2.  Multiple integrals with applications

3.  Vector algebra, lines, planes, and curves in three dimensions

4.  Vector calculus with applications

 

Knowledge Base: 

 

1.        Required Text:  At the level of Stewart, Calculus, 6th edition, Brooks/Cole, 2008. 

2.        Optional Text:  Solutions Guide.

3.    Library Resources: 

·         Apostol, Calculus, Volume I, Blaisdell, Waltham, MA, 1967.

·         Clawson, Mathematical Mysteries:  The Beauty and Magic of Numbers, Plenum, New York, 1996.

·         Danielson, Vectors and Tensors in Engineering and Physics, Addison-Wesley, Redwood City, CA, 1992.

·         Dudley, Readings for Calculus, MAA, 1993.

·         Dunham, The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities, Wiley & Sons, New York, 1994.

·         Easthope, Three Dimensional Dynamics, a Vectorial Treatment, Butterworths, London, 1964.

·         Fraga, Robert (Ed.), Calculus Problems for a New Century, Mathematical Association of America, ISBN #0883850842

·         Halmos, Problems for Mathematicians, Young and Old, MAA, Washington, D.C., 1991.

·         Hight, A Concept of Limits, Prentice-Hall, Englewood Cliffs, N.J., 1966.

·         Knopp, Infinite Sequences and Series, Dover, New York, 1956.

·         Nolan, Women in mathematics: scaling the heights, MAA, 1997.

·         Parker, She Does Math!, MAA, 1995.

·         Sawyer, What is Calculus About?, Random House, 1961.

·         Spivak, Michael, Hitchhiker’s Guide to Calculus, Polished Pebble Press, 1995.

·         Sterrett, 101 careers in mathematics, MAA, 1996.

·         Williamson, Calculus of vector functions, Prentice-Hall, Englewood Cliffs, NJ, 1972.

·         Women, Minorities and Persons with Disabilities in Science and Engineering,  National Science Foundation, 1999 (NS 1.49).

·         Weaver, Conquering calculus: the easy road to understanding mathematics, Plenum, 1998.

·         Young, Excursions in calculus: an interplay of the continuous and the discrete, MAA, 1992.

·         Yount, A to Z of women in science and math, Facts on File, 1999.

4.    Web-based Resources:    

·         Association for Women in Mathematics - http://www.awm-math.org

·         Math Archives -  http://archives.math.utk.edu       

·         The Math Forum - www.forum.swarthmore.edu

·         Waterloo Maple’s Student Center - http://www.maplesoft.com/academic/students/index.aspx

·         Texas Instruments - http://education.ti.com/educationportal/

·         Key Curriculum Press – www.keypress.com

·         Eric Weisstein’s World of Mathematics (Encyclopedia of Mathematics) - http://mathworld.wolfram.com

·         Math Nerds – www.mathnerds.com

·         SOS Mathematics – www.sosmath.com

·         Transformations - www.utc.edu/~cpmawata

·         Intermath – www.intermath-uga.gatech.edu/

·         The Geometry Center - http://www.geom.uiuc.edu

·         Project Interactivate -  www.shodor.org/interactivate 

·         Multicultural Pavilion - www.edchange.org/multicultural

·         Women in Mathematics - www.agnesscott.edu/lriddle/women/women.htm

·         Careers in mathematics -  http://www.ams.org/careers/

5.  Technology Resources:  Maple. 

 

General Expectations:  The student is expected to abide by the university’s attendance policy and honor code.    A maximum of 9 absences are allowed.   If you exceed the maximum allowance and are failing, I may assign you a grade of WF.  If you miss a test for a valid reason, you must notify me on the day of the test or earlier.  Students who initiate withdrawal prior to the withdrawal deadline at midterm, will receive a grade of W (withdrew passing).

 

Disabilities and Accommodations:  North Georgia College and State is committed to equal access to its programs, services and activities for people with disabilities.  If you believe that you have a disability requiring an accommodation, reasonable prior notice needs to be given to the instructor and the Office of Student Disability Resources.  In this case, contact Elizabeth McIntosh, Coordinator, Student Disability Resources at 122 Barnes Hall, 867-2782, emcintosh@ngcsu.edu.

 

Class Evaluations:  Class evaluations at NGCSU are now conducted on-line through Banner.  Evaluation of the class is considered a component of the course and students will not be permitted to access their course grade until the evaluation has been completed.  The evaluations will be accessible beginning one week prior to Final Exam week.

 

Math 2470 Assignment Sheet

 

Lesson

Section

Problems from Section ( Stewart,  Calculus, 6th Ed.)

1

13.1

1 – 39 odd

2

13.2

1- 41 odd

3

13.3

1 – 53 odd, 57

4

13.4

1 – 37 odd, 43

5

13.5

1 – 67 odd, 68 – 76 even

6

14.1

1 – 27 odd

7

14.2

1 – 41 odd, 47, 49

8

14.3

1 – 31 odd, 41 – 45 all

9

14.4

1 – 19 odd

10

15.1, 15.2

1, 7 – 29 odd, 30, 32, 39 – 47 odd, 61, 65    p. 913 / 1 – 19 odd

11

15.3

1 – 7 odd, 11, 15 - 61 odd, 81

12

15.4, 15.5

1 – 7 odd, 11, 25 – 29 odd & p. 943 / 1,5,7,11,13,21,25,27

13

15.6

1 – 33 odd, 39, 41, 43, 47

14

15.7

1 – 19 odd, 41, 43, 45, 51

15

16.1, 16.2

p. 1000 / 1 – 29 odd

16

16.3

1 – 27 odd, 39 – 49 odd

17

16.4

1 – 31 odd

18

16.6

1 – 21 odd, 27

19

16.7

1 – 23 odd

20

16.8

1 – 27 odd, 35

21

16.9

1 – 15 odd

22

17.1

1 – 17 odd, 23, 25

23

17.2

1 – 21 odd

24

17.3

1 – 19 odd

25

17.4

1 – 13 odd

26

17.5

1 – 25 odd, 31

27

17.6

19 – 25 odd, 37 – 45 odd

28

17.7

7 – 15 odd, 19 – 25 odd

29

17.8

1 – 9 odd, 15

30

17.9

1 – 13 odd

Math 2470        Fall Semester 2009

 

Monday

Tuesday

Wednesday

Thursday

Friday

August 17

 

 

18

19

13.1

20

13.1, 13.2

21

13.2

24

13.3

25

26

13.3, 13.4

27

13.4

28

13.5

QOTW

31

13.5

September 1

2

13.5, 14.1

QOTW

3

14.2

4

14.3

QOTW

7

Labor Day

 

8

9

Review

10

Test 1

11

14.3

14

15.1

 

15

16

15.2

17

15.3

18

15.3

QOTW

21

15.4

 

22

23

15.5

24

15.6

25

15.6

QOTW

28

15.7

 

29

30

15.7

October 1

16.1, 16.2

2

16.2, 16.3

QOTW

5

16.3

 

6

7

Review

8

Test 2

9

Fall Break

12

16.3, 16.4

13

14

16.4

QOTW

15

16.6

16

16.6

QOTW

19

16.6

20

21

16.7

22

16.8

23

16.9

QOTW

26

16.9

 

 

27

28

Review

29

Test 3

30

17.1, 17.2

November 2

17.2

 

3

4

17.3

5

17.3

 

6

17.4

QOTW

9

17.5, 17.5

 

10

11

17.5

12

17.6

13

17.7

QOTW

16

17.8

17

18

17.9

19

17.9

20

Review

QOTW

23

Test 4

24

25

26

Thanksgiving Holiday

27

30

Review

December 1

2

Academic Review Day

3

4

Final Exam

10:30 – 12:30