Anne Arundel Community College

Differential Equations 

MAT212, Section 400 – Spring 2015

Class: MW @ 17:10-19:00 in Math-106
Professor:
James Freeman     Office: Mathematics-231-I
Hours:
MW @ 15:00-17:00 ; TTh @ 15:00-16:00
Phone:
(410) 777-2557    Email: jsfreeman@aacc.edu
Website:
http://ola4.aacc.edu/jsfreeman/

Course Description: This is a first course in ordinary differential equations.  The topics include differential equations of various types: separable, exact, linear equations of all orders, and systems of linear equations.  The techniques to be covered include integrating factors, undetermined coefficients, the Wronskian, variation of parameters, reduction of order, power series, Laplace transforms, numerical approximations and matrix methods.  Applications will be selected from kinematic trajectories, mixing, growth, and decay phenomena, vibrating springs, electric circuits and resonance phenomena.  A mathematical software system (Maple) will be an integral and substantial part of the course.

Learning Objectives Upon successful completion of Math 202, a student will be able to:
1. Analyze first-order Initial Value Problems (IVPs) using direction fields and Euler approximations;
2. Solve first-order IVPs including separable, linear, and exact equations;
3. Model various phenomena including mixing, growth, decay, and circuits as first-order IVPs;
4. Solve higher-order linear IVPs;
5. Model various phenomena including springs and electric circuits as higher-order IVPs;
6. Solve higher-order IVPs using power series;
7. Solve higher-order IVPs using Laplace transforms;
8. Solve systems of linear IVPs using both operator and matrix methods;
9. Approximate solutions to IVPs and systems of IVPs using Runge-Kutta methods;
10. Use a mathematical software system to analyze or solve IVPs for equations and systems.

Text: "Elementary Differential Equations" (10th edition) by William E. Boyce and Richard C. DiPrima; Wiley; 2012.

Suggested Further References: 

1.      Differential Equations with Boundary Value Problems by Boyce and DiPrima (more comprehensive edition of the textbook).

2.      Companion website to the text, with instructor and student resources:

  http://www.wiley.com/WileyCDA/WileyTitle/productCd-EHEP002452,descCd-OVERVIEW.html

3.      Differential Equations with Boundary Value Problems by Zill and Cullen.

4.      Differential Equations with Maple by Hunt, Lardy, Lipsman, Osbourn and Rosenberg.

5.      Differential Equations with MatLab by Hunt, Lardy, Lipsman, Osbourn and Rosenberg.

6.   Differential Equations for Dummies.

 

Computer/Calculator: Some work on a computer using Maple is required in this course.  Computers are available in both the Mathematics Building and in the Library.  A graphing calculator is recommended for the course - a TI-84+ is recommended and may be used on tests.  Calculators that perform symbol manipulation, such as the TI-89 or TI-92, are permitted for homework use, but may NOT be used during examinations.

 

Attendance Policy: Regular class attendance is expected and will be recorded.  If you are absent, it is your responsibility to find out what occurred with respect to both announcements and course work.  If you email me, I will respond with that information.  I will maintain an online version of the syllabus on my website.  But even one absence means a lost opportunity to learn.

 

Class Activity: Prepare for class by reading the text (either before or after we cover the material).  If you do not understand something, ask questions in class.  Ask questions even if it concerns material from a prior class or chapter, or, a topic not covered in class.  Asking and answering questions is the main purpose of class.  During class we will review the major points in each chapter and solve sample problems.

 

Homework:   Homework will consist of selected problems from the end of each chapter section in the text.  The homework will be collected and graded.  Late homework loses 10% credit.  Your homework problem solutions should be neatly prepared (they need not be typed), with multiple pages either stapled or otherwise bound together. Answers to the homework are in the back of the book, so there is no reason for a wrong answer.  There is also the Student’s Solution Manual, with explanations of the answers.  With the exception of the Maple projects, the homework will not be graded in detail, but will be reviewed for completeness.  You must show your work and not just give the answer.  If you cannot do or do not understand a homework problem, ask about it in class.  Some homework requires Maple and/or Excel.

 

            Homework assignments will comprise 21% of your grade.

There will be several extended assignments using the Maple software.  In addition, almost every chapter section will require that one problem be worked both with and without using Maple.

(NOTICE:  You cannot receive an "A" for the course if you do not do the homework.)

Examinations: There will be three chapter specific tests and a cumulative final exam.

 

The three tests will comprise 54% of your grade - 18% each.

The final will comprise 25% of your grade.

 

The tests may not be made up (without prior approval).  If you miss a test, the total possible points that the test was worth will be added to the total possible points that the final is worth.  Thus, if you miss a test, your final exam will be worth a larger proportion of your course grade.  I give generous partial credit when I grade, but you must show your work neatly to earn it.  It is your responsibility to show me what you know in a neat and orderly fashion. 

 

Grading Scale: 90 - 100% A; 80-89% B; 70 - 79% C; 60 - 69% D; below 60% F.

 

Additional Help: Do not hesitate to visit me during my office hours.  If my hours conflict with your free time, I will gladly arrange additional times to meet with you.  I am in my office other times during the week so you can always stop by to see if I am in.

 

Academic Integrity: The Anne Arundel Community College Catalog states, "All students are required to exhibit academic honesty in all academic exercises and assignments." This includes cheating, fabrication, facilitating academic dishonesty, and plagiarism.  The instructor has the right and obligation to impose a reasonable academic sanction including, but not limited to, the following:

 

A) Assign a failing grade for the assignment;

B) Assign a grade reduction for the course;

C) Assign a failing grade for the course;

D) Assign an alternative learning experience.

 

I will choose  A  for most situations involving academic dishonesty.  Do not leave the classroom without permission during a test.  If you do, I will collect your test and grade it based upon what you have already finished.  Do NOT use your cell phone during a test.

 

Student Conduct: The Anne Arundel Community College Catalog states; "All students while engaged in college activities shall comply with all college policies and procedures. Students shall conduct themselves in accordance with accepted standards of behavior, respect the rights of others, refrain from conduct or activity which obstructs the work of the college and is damaging to the welfare of the college community or the college." It continues to describe Acts of Misconduct.

 

Cell Phones: Please put cell phones on vibrator mode during class as a courtesy to others.  If you receive a call, I trust that you will leave the room to talk.  Do NOT use your cell phone during a test.

 

Notice of Nondiscrimination: AACC is an equal opportunity, affirmative action, Title IX, ADA Title 504 compliant institution. Call Disability Support Services, 410-777-2306 or Maryland Relay 711, 72 hours in advance to request most accommodations. Requests for sign language interpreters, alternative format books or assistive technology require 30 days' notice.  For information on Anne Arundel Community College's compliance and complaints concerning discrimination or harassment, call Kelly Koermer, J.D., AACC's federal compliance officer, at 410-777-2607 or Maryland Relay 711.

 

Course Schedule (All dates are tentative.)

 

Dates                         Assignments

 

Jan 21                         First Class

Feb 02                         Chapter 1 Homework Due

Feb 23                         Chapters 2 Homework Due

Feb 25                         Chapters 8 Homework

Mar 02                        Examination on Chapters 1 & 2 & 8

Mar 04                       Maple-I Due

Mar 30                       Chapters 3 Homework Due

Apr 06                        Chapters 4&5 Homework Due

Apr 13                        Examination on Chapters 3 & 4 & 5

Apr 22                        Chapter 6 Homework & Maple-II Due

Apr 28                        Chapter 7 Homework Homework Due

Apr 28                        Examination on Chapters 6 - 7

 

May 13                      Maple-III Due

                                   Review and additional topics as time allows

 

May 18 (Mon)           Final Examination (17:00 - 19:00)

 

Jan 28                        Last day to drop with full refund

Mar 16-20                 Spring Break

Apr 21                        Last day to withdraw

 

Homework Assignments

 

1. Introduction to Differential Equations

1.1: 1,3,5,6,10,11,25                                       1.2: 1,5,7,9,13,17

1.3: 1,3,5,7,11,17,19,29,30                             1.4: Read

 

2. First Order Differential Equations

2.1: 13,17,21,31,38                                        2.2: 1,5,7,13,19,21,29

2.3: 1,3,5,7,13,23,32                                      2.4: 1,3,5,9,13,27

2.5: 1,20*,25*                                                2.6: 1,5,9,19,21,25

2.7: 1,3,5,7                                                     2.8: 1,2

                                                          

8. Numerical Methods

8.1: 1,3                                                           8.2: 1,3

8.3: 1,3

 

3. Second Order Linear Differential Equations

3.1: 1,3,7,9,10,15,21                                      3.2: 1,3,5,13,17,25

3.3: 1,3,9,13,17,19,23,34                               3.4: 1,5,7,11,13,15

3.5: 1,5,9,15,19                                              3.6: 3,5,13,15 (Optional)

3.7: 5,7,15,17,21                                            3.8: 5,7,15,17

 

4. Higher Order Linear Differential Equations

4.1: 1,3,5,7,9,11,13,17                                   4.2: 11,12,16,32,39

4.3: 1,3,5,9                                                     4.4: 1,3,5 (Optional)

 

5. Series Solutions of Second Order Linear Differential Equations

5.1: 1,5,9,15,21,27                                          5.2: 1,3,7,15,21

5.3: 1,5,7,10                                                    5.4-7: TBD

 

6. The LaPlace Transform

6.1: 1,3,7,9,15,23,25,30                                   6.2: 1,5,9,11,15,22

6.3: 7,9,11,13,19,36*,37*                                6.4: 1,3,5,7

6.5: TBD                                                           6.6: TBD

 

7. Systems of First Order Linear Differential Equations

7.1: 1,5,9,19,21                                                7.2: 11,13,15,17,22*,23*

7.3: 7,9,11,17,19,20,23                                    7.4: TBD

7.5: 1,5,11,15,32*,33*                                     7.6: 1,3,5,9

7.7: 1,3,7,11                                                     7.8: 1,3,9,11,12,16

7.9: 1,5,8