Introduction to Ordinary Differential Equations

MATH 30613

Spring 2008

 

The calculus is the greatest aid we have to the application of physical truth

in the broadest sense of the word.- Osgood, W. F.

 

Course Web Site:                              http://faculty.tcu.edu/gfriedman/ODE

Instructor:                           Greg Friedman

e-mail:                                 g.friedman@tcu.edu

Office:                                 309 Tucker Technology Center

Phone:                                 X6343

Office Hours:                     Official office hours are to be determined, but I'm usually around most afternoons until 6 or 7 PM, so feel free to drop by. We can also make specific appointments, or you can ask questions by e-mail.

 

Class Schedule:                  MWF 10:00-10:50 in TTC 352

Final Exam:                         Friday, May 9, 8:00-10:30 AM

Required Text:                    Differential equations by P. Blanchard, R. Devaney, and G. Hall, 3rd edition, with included CD ROM.

Prerequisites:                     Students are expected to be proficient in the material of Calculus I and II.

 

Asking questions:               Ask questions in class! It helps me know what needs to be explained better, and it makes classmates grateful that someone had the courage to ask. You are also encouraged to ask questions before class, after class, in my office hours, by e-mail, over telegraph, and every other possible way. Don't be shy!

 

COURSE OBJECTIVES:

(1)    Learn what differential equations are and become familiar with qualitative, numerical, and quantitative methods of solving them.

(2)    Gain experience working with and critically evaluating different mathematical models.

        (3)    Improve your quantitative literacy, problem solving skills, and mathematical confidence.

        (4)    To have fun while working hard and learning some challenging material.

Calculators:  Most of the assignments will not require you to use calculator. Occasionally a simple graphing calculator might be helpful. You may not use TI 89 calculators and other calculators with symbolic capabilities during examinations.

 

Course Policies and Procedures

Exams: There will be three in-class midterm exams – see calendar below. The final exam will be on Friday, May 9, at 8:00 AM.

Problem assignments: Homework problems will be assigned via the course website at http://faculty.tcu.edu/gfriedman/ODE/hw.html . Problems will be listed by textbook section and due at the the beginning of the second class session following completion of the relevant material in class. For example, homework assigned on material covered in class on Monday will be due on Friday. You may discuss homework problems with others and are encouraged to come to me for help either during my office hours, by appointment, or whenever you can catch me around. You may collaborate on homework problems, BUT solutions must be written up individually. In other words, you may work in groups in attempting to solve problems, but you must write up solutions on your own and demonstrate your own mastery of the solution. It is imperative that you learn the material for yourself; there will be no collaboration on exams. Late problem sets will not be graded.

Grading: Your final average will be determined approximately as follows: 30% for the final exam, 20% for each midterm, and 10% for homework. Grades will be curved somewhat at the end of the semester, but a cumulative average of 90% or above guarantees at least an A-, a cumulative average of 80% or above guarantees at least a B-, a cumulative average of 70% or above guarantees at least a C-, and a cumulative average of 60% or above guarantees at least a D-.

Attendance: Attendance is expected. You are responsible for all material and information from all class sessions. If you plan to miss class, even with a University Excused Absence, you are responsible for letting me know as far in advance as possible.

Make-ups: In the event that you will be unable to take an exam or quiz on time, a written excuse is required. I expect to be notified in advance except in the case of serious emergency, and in all cases I expect to be notified as soon as reasonably possible. Excuses may also be given to hand in homework late, again provided that a reasonable request is made in advance or proof of emergency situation is presented. Failure to abide by this policy may result in loss of course credit.

Extra help: In addition to help from me, students may seek extra help from the math clinic or through tutoring. Students whose grade average drops below passing will be required to seek extra help and to provide documentation if that help is sought outside of my office hours.

 

Course Schedule and Syllabus

 

Syllabus: We will cover roughly Chapters 1 through 4 and Chapter 6 of the text, topics including basic mathematical modeling, first and second order differential equations, systems of linear equations, and Laplace transforms.

The following calendar should be taken as a rough guideline, subject to much change:

 

Week

Start Date

Topics

Special

1

Jan. 14

Sections 1.1-1.2

 

2

Jan. 21

Sections 1.3-1.4

 

3

Jan. 28

Sections 1.5-1.6

Feb. 2- Groundhog's Day

4

Feb. 4

Sections 1.8-1.9

 

5

Feb. 11

Sections 2.1-2.2

Midterm 1 – Feb. 15

6

Feb. 18

Section 2.3

 

7

Feb. 25

Sections 3.1-3.2

 

8

Mar. 3

Sections 3.3-3.4

Mid-semester, March 5

9

Mar. 10

 

Spring Break (Woohoo!), March 14- Pi Day

10

Mar. 17

Sections 3.5-3.6

Midterm 2, March 19; Good Friday, March 21

11

Mar. 24

Sections 4.1-4.2

 

12

Mar. 31

Sections 4.3-4.4

 

13

Apr. 7

Sections 6.1-6.2

Midterm 3 - April 11

14

Apr. 14

Sections 6.3-6.4

 

15

Apr. 21

Section 6.5

 

16

Apr. 30

Review

Last Day of Classes – Apr. 30

17

 

 

Final Exam – Fri., May 9, 8:00 AM

 

 

 

 

University Policies:

 

Statement on Disability Services at TCU: Texas Christian University complies with the Americans with Disabilities Act and Section 504 of the Rehabilitation Act of 1973 regarding students with disabilities.  Eligible students seeking accommodations should contact the Coordinator for Students with Disabilities in the Center for Academic Services located in Sadler Hall, 11.  Accommodations are not retroactive, therefore, students should contact the Coordinator as soon as possible in the term for which they are seeking accommodations. Further information can be obtained from the Center for Academic Services, TCU Box 297710, Fort Worth, TX 76129, or at (817) 257-7486.

Academic Misconduct (Sec. 3.4 from the Student Handbook) – Any act that violates the academic integrity of the institution is considered academic misconduct. The procedures used to resolve suspected acts of academic misconduct are available in the offices of Academic Deans and the Office of Campus Life.  Specific examples include, but are not limited to:

  • Cheating: Copying from another student’s test paper, laboratory report, other report, or computer files and listings; Using, during any academic exercise, material and/or devices not authorized by the person in charge of the test; Collaborating with or seeking aid from another student during a test or laboratory without permission; Knowingly using, buying, selling, stealing, transporting, or soliciting in its entirety or in part, the contents of a test or other assignment unauthorized for release; Substituting for another student or permitting another student to substitute for oneself;
  • Plagiarism: The appropriation, theft, purchase or obtaining by any means another’s work, and the unacknowledged submission or incorporation of that work as one’s own offered for credit. Appropriation includes the quoting or paraphrasing of another’s work without giving credit therefore.              

·        Collusion: The unauthorized collaboration with another in preparing work offered for credit.

 

Netiquette: Communication Courtesy Code.  All members of the class are expected to follow rules of common courtesy in all email messages, threaded discussions and chats.  If I deem any of them to be inappropriate or offensive, I will forward the message to the Chair of the department and the online administrators and appropriate action will be taken, not excluding expulsion from the course.

 

Email Notification: Only the official TCU student email address will be used for all course notification. It is your responsibility to check your TCU email on a regular basis.

 

This syllabus represents my current plans and objectives.  As we go through the semester, those plans may need to change to enhance the class learning opportunity.  Such changes, communicated clearly, are not unusual and should be expected.