**Anne Arundel Community
College**

**Differential
Equations**

**Class:**** MW @ 17:10-19:00 in Math-106****Professor:**
James Freeman

Hours:

Phone:

Website:

**
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.

** **

**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.**

**
(NOTICE:
**

**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 **

**Apr 13 Examination
on Chapters 3 & 4 & 5**

**Apr
22 Chapter
6 Homework & Maple-II
Due**

**Apr 28 Chapter
7 Homework
**

**Apr 28** ** Examination
on Chapters 6 - 7 **

** **

**May 13 **

**
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