ORDINARY DIFFERENTIAL EQUATIONS, MTH254-22W, (CRN: 62146.202406), SUMMER 2024

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ORDINARY DIFFERENTIAL EQUATIONS, MTH254-22W, (CRN: 62146.202406), SUMMER 2024

Course Description (what this whole course is about)

This course covers the methods of solving ordinary differential equations and applications in engineering and the sciences.  Topics include equations of the first order, higher order equations, power series solutions and applications.

Student Learning Outcomes (what you’ll be able to do after this course)

1. Solve First-Order Differential equations of the following types: Separable equations, Homogeneous equations, Exact equations, and Linear equations.

2. Solve Second-Order Homogeneous Linear equations with constant coefficients, and solve non-Homogeneous equations by the superposition approach.

3. Use the Laplace transform to solve linear first-order and second-order differential equations with constant coefficients.

4. Find Power Series solutions about the ordinary point of a differential equation.

5. Solve systems of differential equations using the Operator method, and using the Laplace transform method.

6. Solve initial-value problems and work with the applications of using the differential equations model to describe some real-life phenomena. These include growth/decay problems, carbon-dating problems, and half-life problems. These also include using a second-order differential equation to interpret simple harmonic motion and free damped motion in a vibrating spring-mass system.

7. Locate an approximate solution curve for a First-Order differential equation in a direction field and approximate solutions of the first-order initial-value problems using the numerical methods.

Instructional Objectives

Throughout this course you will use your MTH214 Calculus I and MTH215 Calculus II skills to solve differential equations. This course is a combination of learning methods to solve differential equations mixed in with applications and real-world problems that require differential equations to solve. A strong background in differentiation and integration will help you greatly in this course.  This course is organized with effective teaching in mind. The course materials and assessments (quizzes, discussions, assignments) are focused on these objectives so that by the end of a successful semester you will have the opportunity to gain the following knowledge and skills: solve various differential equations and use differential equations to model and then study real-world problems.

Required and/or Supplemental Materials

The required textbook for this course is:

A First Course in Differential Equations: The Classic Fifth Edition, Fifth Edition by Dennis G. Zill; Brooks/Cole, Cengage Learning.

ISBN 10: 0534373887  ISBN 13: 9780534373887

This book is a classic, time-tested book that is fairly easy to read and provides the reader with plenty of examples.  Each week we will cover a few sections from the book.  The homework will also come from this book.

The book selected for our course is available through the Bristol Bookstore or alternative booksellers. If you normally use a book voucher from financial aid, you should buy your books from the Bristol Bookstore. Often, materials may be purchased or rented used, new, as hardcopy or digital versions at various prices. Additionally, materials may be borrowed or on reserve at the library at no cost to you. Search for books on the library homepage or contact them at 774.357.2108 or [email protected]. If the cost of books is a barrier to purchasing them, please email me or speak with me during office hours.

In the online space, I have also selected videos and appropriate supporting documents that will help you learn the material.

Teaching Procedures (how I teach this course)

Since our course is fully online asynchronous, we will not meet at specific times. This means that you can complete your coursework from anywhere at your convenience, within the time frame provided for submissions. To make this class easy to manage, the class will be organized in weekly modules.  Each week I will list out the sections to be covered and provide a plan through the material.  This online course is modeled after a 1-night per week in-person Ordinary Differential Equations course.  This class would generally meet on Thursdays for roughly 3 hours a night.  I recommend you use this schedule to plan your coursework for the week.

Generally, each week you will read sections of the book, try examples from the textbook, and do homework problems that are like the examples. I will also provide supporting material such as notes, OER books (where available), section and chapter summaries, and links to videos. The purpose of the material is not to overwhelm you, but to provide more supporting material that can offer a different perspective than what you see in your textbook. The content on e-Learning is a digital notebook that you can refer to. A homework set will be assigned each week.

To be successful in the course, follow: Learn > Practice > Assess.  Differential Equations problems require practice to get the techniques mastered. I am here to help.

Whenever necessary, an optional synchronous Zoom session may be arranged. Remember, even though we will not meet at specific times, I am available to you during by email, telephone, or Zoon.

Criteria for Evaluating Student Performance

All Instructors are required to include this section to meet the Syllabus Checklist criteria. List your grading criteria below.

CRITERIA	PERCENTAGE
Exam 1	18.75%
Exam 2	18.75%
Exam 3	18.75%
Homework	18.75%
Final Exam	25%

To summarize:

Three one-hour exams and assignments/homework – 75%

(Total is considered as four exams, worth 75% of your final grade. Hwk grade is designed to help your test grades.)

Final exam – 25%

Exams:

There will be three exams and one longer exam, a Final exam. The exams will be very similar in style to the homework problems you solve.  Generally, differential equations problems are long and require time.  As such, most exams will consist of roughly 5-6 problems.  As in most math classes, the steps and technique of solving the problems are most important. I give partial credit if you are able to clearly work through the problem but arrive at the wrong answer. I do not formally drop the lowest exam, though I will work with your grades at the end of the semester if there is one grade that is extremely low. There is room for scaling.

On the day of the exam, I will post the exam and you will have the day to work on it.  Hour exams will consist of short answer questions concerning terminology and theory and problems similar to homework problems covering application of theory.  To prepare for hour exams study lecture notes, assigned readings and homework problems.  Exams are tentatively scheduled for: Thursday 6/27, Thursday 7/18, Thursday 8/8, Final - Thursday 8/22.

After-the-fact make-up tests will only be allowed for emergency circumstances approved by the instructor. If you know in advance that you will be unable to take a test on time (e.g., funeral, jury duty, family vacation, etc.), you must contact the instructor, in advance, to arrange an alternate test schedule. If for any other reason you fail to submit a test on time, the grade will be zero.

Homework: Homework assignments will generally be the odd numbered problems in each section covered, subject to additions and deletions.  Since the best assurance of success in any mathematics course is to do the daily assignments faithfully when assigned, these assignments will be submitted and counted in the final grade. Each assignment must be labeled at the top of each page with assignment number, page number and problems, and the student’s name.  It is recommended that a loose-leaf notebook be used for keeping homework papers.

I realize that there are answers to the odd problems in the back of the book, as well as solution manuals, and websites that provide major steps to many of the problems assigned for homework. Many of these solutions leave out vital steps or use tricks that are easily forgotten by semester’s end.  The homework is meant for you to practice the material covered in course. I encourage all students to follow methods I teach to solve the problems, with the goal of practicing them for themselves. Please rely on solution manuals only when needed.  I am here to teach you the best methods of solving these problems, with all steps done clearly out. Homework simply copied from solution guides will not be accepted.

Late Submissions

Homework is worth 2 points if you make an effort to try each problem and submit on time.  Homework is an opportunity to learn, and as such, making errors and having incorrect answers is a normal part of the process, and will not lower your grade.  Homework is where you practice the problems, so you will not be graded on correct answers, effort only.  As such, the work for each problem must be shown, no credit for answers only.  Late assignments will be accepted until the date of the exam covering that material but will count for less credit (1 pt) than a well-done assignment handed in on time.

SUCCESS:

Differential Equations problems tend to be long!  A missed step or a mistake early on can cause much wasted time and effort!

1. Try to do all problems out neatly.

2. Follow the patterns step-by-step, one step at a time, as done in class.

3. Give yourself plenty of room.  Use one sheet of paper per problem.

Basis for Student Grading

Explore Grading Policies for policy information regarding this section. At the end of the semester students will receive one of the following letter grades based on their performance:

A+ = 97-100%	A = 93-96%	A- = 90-92%	B+ = 87-89%	B = 83-86%	B- = 80-82%
C+ = 77-79%	C = 73-76%	C- = 70-72%	D+ = 67-69%	D = 63-66%	D- = 60-62%
F = 0-59%	WF=0-59%

Attendance and Participation

Attendance is important to student success.  Yes, we track your participation in online course.

Canvas: In an online course, it is not enough to just “log in” to the class on a weekly basis. Students MUST be actively participating in a meaningful way in the weekly online discussion boards and making submissions to all weekly assignments.

Contingency: Bristol Community College provides all students with a free Microsoft OneDrive account with 1 TB of storage for preserving college related material. SAVE your syllabus, reading material, assignments, due dates, contact information just in case you need it and you don’t have access to this site. In case of emergency, the solar canopies on the Bristol Fall River Parking lot also serve as internet hot spots, so you don’t need to miss deadlines. ALWAYS be in touch with me about anything interfering with your ability to complete work on time.

Also, read Student Course Attendance and Participation for in-depth information, or contact the Registrar’s Office at 774-730-2250 or [email protected].

Time Considerations

Structuring your time for learning is an important part of college success. To effectively balance time between school and non-school activities, plan a schedule with the time considerations below.

Each day contains 24 hours which adds up to 168 hours in a week.

· For 15 week 3-credit courses, plan to spend 9 hours a week per course.

· For 11 week 3-credit courses, plan to spend 12 hours a week per course.

· For 6 week 3-credit courses, plan to spend 23 hours a week per course.

· For Wintersession 3-credit courses, plan to spend 45 hours a week per course

Since our course is a 15 week 3-credit course, I expect you to use 9 hours a week to be successful in the course.

Withdrawal Policy

Students are responsible for withdrawing officially if they stop attending any or all classes. A grade of “WF” will be assigned to any student who stops attending a course but does not officially withdraw.

Students that are looking to withdraw from one or more of their classes should reach out to their assigned advisor prior to doing so. Their advisor will explain how withdrawing will affect them because withdrawing may affect Satisfactory Academic Progress and can place the student at risk for academic probation or dismissal; See Satisfactory Academic Progress (SAP) in the Academic catalog. Students who use financial aid and who subsequently withdraw may be required to return some or all funds received. Failure to comply may result in ineligibility to receive future financial assistance at any institution, referral to collections agencies, and interception of income tax refunds.

Please see the full Withdrawal Policy & Procedures page for more information. If a student is not assigned an advisor, then they should be directed to the advising center. Students can find their assigned advisor in their degree works page.

Watch How to Find Your Assigned Advisor for more details or locate DegreeWorks in accessBCC. Visit the Advising webpage to schedule an appointment with your assigned advisor today.

Interaction and Communication Plan

Instructor Communication

• Questions regarding any aspect of the course should be brought to the attention of the instructor from the student’s bristolcc.edu email account to the instructor at [email protected].  Please use a descriptive email subject line with a note to this course MTH254.

• The instructor will attempt to respond to all questions as soon as possible, and within 24 hours, during the Monday to Friday work week. I check my email daily Monday through Friday during normal business hours only. You can expect email response within 24-48 hours during the work week. You *may* get an email reply during the weekend, but that would be an exception not the rule.

Face-to-Face Communication:

•   While this course is an online course, students who are able to, and wish to, may also contact me to discuss meeting face-to-face.

•   Students may also meet electronically with the instructor using Zoom (similar to Skype) through the course space.

Student Participation

In this online course, evidence of interaction is required. Interaction includes communications and meetings between instructor and students as well as between students. Attendance is measured by your participation, so it is important that you actively participate in our course. Active participation includes completing weekly online discussion boards, making submissions to weekly assignments, and/or communicating with me to ask course-related questions. If you find that you cannot be an active participant in the course for any reason, please contact me so we can discuss your options.

Behavior Toward Others

Learning thrives in an atmosphere of mutual respect and cooperation. In order to learn, we must be open to the views of people different from ourselves. In our course, honor the uniqueness of your classmates and appreciate this time we have to learn from one another. Please treat your colleagues and me with respect, and for the safety and well-being of all, respect others’ opinions and avoid personal attacks or demeaning comments. For more information, see the Bristol Netiquette Policy