Mathematics & Computer Science Department                                          

Syllabus for Math 3000,   Differential Equations 

Dr. Green              egreen@ngcsu.edu                                             Office:  Newton Oakes 222            (706) 864-1809

Fall 2009                                                                                               Office Hours:       9:00 – 11:00  MWF & 4:30 – 5:30 MW,

                                                                                                                1:15 – 2:15 TR,     or by appointment

 

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

 

Catalog Description:  An introductory course in ordinary differential equations with emphasis on linear differential equations of the first and second orders.  Topics include solution of second order differential equations by the methods of undetermined coefficients, variation of parameters, and Laplace transforms.

 

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

·         Determine an appropriate method of solution of a first or second order differential equation.

·         Solve first and second order differential equations by methods developed in the course.

·         Determine the existence and uniqueness of solutions to an initial-value problem.

·         Model an applied problem by setting up an initial-value problem.

·         Interpret the solution of an applied problem in the context of the situation.

·         Determine the long-term behavior of solutions of differential equations.

·         Solve mass on spring problems involving free-undamped, free-damped, and forced motion.

·         Classify the damped mass on spring motion as underdamped, critically damped, or overdamped.

·         Solve differential equations which are non-routine by using the problem-solving approaches employed during the course.

·         Use the correct notation and terminology when communicating results in the area of differential equations.

·         Find the Laplace transform or inverse Laplace transform of a given function.

·         Solve an initial-value problem by using Laplace transforms.

·         Explain mathematical proofs in the area of differential equations.

·         Describe real-world applications of differential equations.

 

 

Methods of  Instruction:  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: 

                                Test Average:       2/3  or  1/3   (2/3 if higher than final exam) Avg includes 3 tests & QOTW total 

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

                                2 extra credit computer assignments will be given. .  Points earned will be added to a test grade.

 

Course Content:   See catalog description and calendar.

 

 

 

 

 

Knowledge Base: 

 

1.  Required Text: At the level of Zill, A First Course in Differential Equations with Modeling Applications, 8th  Ed., Brooks/Cole, 2005.

 

2.  Supplementary Text:  None.

 

3.  Library Resources: 

 

·         Birkhoff, Ordinary differential equations, Wiley, 1989.

·         Differential Equations Models in Biology, Epidemiology, and Ecology, Lectuer Notes in Biomathematics, Springer-Verlag, New York, 1991.

  • Dunham, The Mathematical Universe: An Alphabetical Journey Through the Great Proofs, Problems, and Personalities, Wiley & Sons, New York, 1994.
  • Halmos, Problems for Mathematicians, Young and Old, MAA, Washington, D.C., 1991.
  • Hubbard and West, Differential Equations, a Dynamical Systems Approach, Springer-Verlag, New York, 1991.
  • King, Differential Equations:  linear, nonlinear, ordinary, partial, Cambridge, 2003.
  • Lefschetz, Differential Equations: Geometric Theory, Dover, New York, 1977.
  • Nolan, Women in mathematics: scaling the heights, MAA, 1997.
  • Parker, She Does Math!, MAA, 1995.
  • Spiegel, Applied Differential Equations, 2nd edition, Prentice-Hall, Englewood Cliffs, NJ, 1967.

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

  • Vladimirov, Equations of Mathematical Physics, M. Dekker, New York, 1971.
  • Women, Minorities and Persons with Disabilities in Science and Engineering,  National Science Foundation, 1999 (NS 1.49).
  • 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

·         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/

·         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.  Attendance:   For TH classes, a maximum of 5 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.  Withdrawal Policy:  Students who initiate withdrawal prior to the withdrawal deadline at midterm, will receive a grade of W (withdrew passing).

 

 

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.  Specific instructions will be made available when the surveys are activated. 

 

 

 

 

Disabilities and Accommodations.  North Georgia College and State University 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.

 

 

 

 

 

Math 3000 Differential Equations

Assignment Sheet

 

 

Assignment     Read           Problems_________________________

      1        1.1            1-35 odd

2        1.2            1 – 33 odd             

1.3                                                (no problems assigned)

 

      3        2.1            1,3,5,7

      4        2.2            1-27 odd, 35, 37, 41

      5        2.3            1-33 odd, 45

      6        2.4            1-35 odd

      7        2.5            1-13 odd          

      8        3.1            1-19 odd

      9        3.1            21 – 27 odd, 35, 43

     10        3.2            2, 3, 9, 11, 13, 15

         

     11        4.1.1          1-13 odd        

     12        4.1.2          15-29 odd      

     13        4.1.3          31-37 odd

     14        4.2            1-17 odd

     15        4.3            1 – 39 odd, 43, 45, 47

     16        4.4            1-31 odd, 41

     17        4.6            1-19 odd, 23

     18        4.7            1-21 odd, 31, 39

 

     19        5.1.1          1-11 odd, 15

     20        5.1.2          17-27 odd

     21        5.1.3          29-33 odd  

    

     22        7.1            1 - 41 odd

     23        7.2.1          1 – 29 odd

     24        7.2.2          31 – 39 odd

     25        7.3.1          1 – 19 odd

     26        7.3.1/7.3.2    21 – 29 odd, 37 – 61 odd

     27        7.3.2          63 – 71 odd

     28        7.5            1 – 9 odd

 

 

 

Text: Zill, A First Course in Differential Equations with Modeling Applications, 9th edition.

 

 

 

 

 

 

 

 

 

 

 

 

Math 3000          Fall Semester 2009

 

Monday

Tuesday

Wednesday

Thursday

Friday

August 17

 

 

18

19

1.1

20

21

1.2

24

1.2, 2.1

25

26

2.2

27

28

2.3

31

2.3, 2.4

September 1

2

2.4

3

4

2.5

7

Labor Day

 

8

9

3.1

10

11

3.1

14

3.2

 

15

16

Review

17

18

Test 1

21

3.1, 4.1.1

 

 

22

23

4.1.2, 4.1.3

24

25

4.2

28

4.3

 

29

30

4.3, 4.4

October 1

2

4.4

5

4.6

 

 

6

7

4.6

8

9

Fall Break

12

4.7

13

14

4.7, 5.1.1

15

16

5.1.2

19

5.1.3

20

21

Review

22

23

Test 2

26

7.1

27

28

7.1, 7.2

29

30

7.2

November 2

7.2

 

3

4

7.2, 7.3

5

6

7.3

9

7.3

 

10

11

7.3

12

13

7.5

16

7.5

17

18

19

20

Test 3

23

Review

24

25

26

Thanksgiving Holiday

27

30

Review

December 1

2

Academic Review Day

3

4

Final Exam

3:30 – 5:30

7

8

9

10

11