Welcome! I’m James Boffenmyer and I will be your online instructor for Math 224 - Differential Equations! I am looking forward to working with you this semester. Please read the following topics below that can be very helpful for our course!
If you need to ask any questions, the Canvas inbox is the easiest way to do it. However, if you have trouble with that, my email is listed below.
Email: jrboffenmyer@frc.eduI’ll typically respond within 24-48 hours.
My office hours for Spring 2026 are on Fridays from 1pm - 2pm. There may be instances where I need to change them, but I will notify the class via Canvas Announcements.
Office Hours in online classes do not mean that I will be visibly present in a Zoom room during this time (because I do not want you to feel obligated to take time out of your day to attend). It simply means that I will be available to answer any and all questions that you may have. This could be accomplished through Email, Zoom, and/or Canvas messaging.
In online classes, it’s easy to feel isolated and left out there stranded. Therefore, we have a discussion in the course that can help “break the ice”, but I always like to get started first on that.
To start off, you have the biggest nerd for a teacher! I wear that honor
with pride!
My educational background is pretty vast, but I love learning.
It may seem like I have more degrees than a thermometer, one huge benefit of working at a university is the ability to learn for almost free. We have an amazing discount within our University system that allows us to work for a degree for pennies on the dollar. I love being a lifelong student, but I’m not going into debt for it.
While learning is my passion, my wife is a high school mathematics teacher and I am a father to a 8-year-old little boy (Jacob) a 5-year-old little girl (Camilla) and a 1-year old boy (Andrew). Needless to say life is nonstop!!!
“Be yourself; everyone else is already taken.” - Oscar Wilde
4 Hour Lecture Course (68-72 hours) Delivered Online using Canvas
This course is an introduction into ordinary differential equations including both quantitative and qualitative methods as well as applications from a variety of disciplines. This course focuses on linear differential equations and their applications to sciences and engineering. The laws of nature may be expressed as differential equations.
At the conclusion of this course, you will be able to:
“Success is Dependent on Effort” - Sophocles
No textbook will be required for this course. All problems, examples, etc will be provided by the instructor in the form of Open Educational Resources.
Computer Programs that are highly recommended:
LaTeX : This is used for typesetting Mathematical documents. This is a good language to know because Canvas’ math editor uses this in the programming.
Python: Can be used to solve general Differential Equation & Plotting Direction Fields
RStudio: Can be used in place of LaTex. Has LaTeX built into this program; keeps you from knowing much of the LaTeX syntax. This syllabus is built in RStudio.
To enroll and participate in classes online, you must use a personal desktop computer or laptop (PC or Mac) with at least 8 GB of random access memory (RAM) and 60 GB of free hard-drive space (additional space may be needed for course-related files).* It is also required to have a sound card with speakers, webcam and microphone for assignments, communication and examination.
In an online learning environment, computer software and hardware allow you to communicate clearly and effectively with faculty, staff, and other students. It is the vehicle by which you submit all course assignments. Without the appropriate software and hardware, you will not be able to access course materials, collaborate with faculty, and complete assignments for submission and grading.
The use of public access computers (for example public library
computers) may not permit access to certain course materials or systems
due to security limitations.
Because online learning tools are mobile responsive, students may use
mobile devices such as tablets (e.g., iPad), mobile phones, and notebook
computers (e.g., Chromebooks) to perform some academic activities and
thereby supplement the use of a desktop computer or laptop. However, a
desktop computer or laptop must remain your primary device for
studies.
Please note that to install and use mobile apps for your studies, your mobile device must meet the apps’ hardware, storage, and data requirements. Data rates may apply; check with your mobile service provider.
*Please note: Technical Support is not available to offer guidance or technical support concerning the use of microphones or webcams. Students should understand how to operate the built-in features and/or external equipment prior to using them in the classroom environment.
All courses require Microsoft Office (specifically Microsoft Excel, Word, and Powerpoint). The student may use the school-provided Microsoft Office 365 online version or a personal license of Microsoft Office 2010 or more current.
Cookies should be enabled.
“However difficult life may seem, there is always something you can do and succeed at.”
- Stephen Hawking
The topics that we’ll cover in this course are:
Other topics relating to the course learning outcomes may be included to best prepare you for the next level of coursework.
This is the schedule that we’ll follow throughout this semester. Keep in mind, things may change due to unforseen circumstances, such as weather cancellations, cyber security issues, etc. Changes to the schedule will be announced via Canvas Announcements.
The open times for the assignments are 12:01am PST on the date listed below. The close times for the assignments are 11:59pm PST on the date listed below.
There are a few weeks between modules, so this should give you ample time to work on this material. Please do not procrastinate.
| Module Number | Assignment Name | Learning Objective | Due Date |
|---|---|---|---|
1 |
Introduction to Differential Equations Classification of Differential Equations Module 1 Homework Module 1 Discussion Module 1 Quiz |
CLO 1 | Opens on Jan. 21, 2026 Closes Feb. 8, 2026 |
2 |
Linear Differential Equations Separable Differential Equations First-Order Differential Equations Exact Differential Equations Integration Factors Module 2 Homework Module 2 Discussion Chapter 2 Quiz |
CLO 2 and 3 | Opens Feb. 9, 2026 Closes Mar 1, 2026 |
| Examination 1 | CLO 1, 2, and 3 | Opens on Feb. 23 Closes on Mar. 1 |
|
3 |
Homogeneous Differential Equations with Constant Coefficients Linear Homogeneous Equations Complex Roots of Characteristic Equations Method of Undetermined Coefficients Variation of Parameters Module 3 Homework Module 3 Discussion Module 3 Quiz |
CLO 4 | Opens Mar. 2, 2026 Closes Mar. 22, 2026 |
4 |
nth-Order Linear Differential Equations Homogeneous Differential Equations with Constant Coefficients Method of Undetermined Coefficients Method of Variation of Parameters Module 4 Homework Module 4 Discussion Module 4 Quiz |
CLO 7 | Opens Mar. 23, 2026 Closes Apr. 12, 2026 |
| Examination 2 | CLO 4 and 7 | Opens Apr 6 Closes Apr. 12 |
|
5 |
The Laplace Transform Solutions to Initial Value Problems Step Functions Differential Equations with Discontinuous Forcing Functions Impulse Functions Module 5 Homework Module 5 Discussion Module 5 Quiz |
CLO 4 and 6 | Opens Apr. 13, 2026 Closes May 3, 2026 |
6 |
Systems of First-Order Linear Equations Matrices Systems of Linear Algebraic Equations, Linear Independence, Eigenvalues, Eigenvectors Theory of Systems of First-Order Linear Equations Homogeneous Linear Systems with Constant Coefficients Module 6 Homework Module 6 Discussion Module 6 Quiz |
CLO 5 and 7 | Opens May 4, 2026 Closes May 17, 2026 |
| Comprehensive Final Exam | CLO 1 through 7 | Opens May 18 Closes May 22 |
| Assignment Category | Percentage Weight |
|---|---|
| Discussion Topics | 15% |
| Quizzes | 5% |
| Homework | 25% |
| Teaching Demonstration | 20% |
| Examinations | 15% |
| Final Examination | 20% |
There will be a discussion thread for each topic. Each discussion will be graded out of a maximum of 100%.
There are two parts to your discussion posts:
The initial posts are due by Thursday at 11:59pm PST and your responses to other classmates are due by Sunday at 11:59pm PST.
There will be homework assignments for each topic. While each assignment does not have a huge impact on your grade, it serves as practice for the examinations, which do have a large impact on your grade.
There will be a quiz for each module to assess how well you understand the topics at hand for that part of the course.
The allotted time, question types, and amount of questions for each exam will vary. The information will be made in an announcement prior to the Exam opening. It is your responsibility to keep track of the announcements and/or the schedule on the syllabus.
This assignment serves as a “Capstone” assignment for the course. It will assess not only how well the student knows the material, but how they can explain it. The teaching demonstration will be graded out of a maximum of 100%. This assignment will be 20% of the overall grade in the course.
Topics will be provided by the Instructor via Canvas
This is the final assessment of the course. The Comprehensive Final Exam will be graded out of a maximum of 100%. This assignment will be 20% of the overall grade in the course.
This institution does not have an official policy for the use of artificial intelligence (AI) and language model text generators like ChatGPT, but this course does.
While this institution recognizes that such tools can assist in writing and solving problems, such toolsare NOT a replacement for your own creativity, originality, or critical thinking.
Such skills require time and effort to develop. Thus, the use of these tools without the instructor’s consent constitutes a violation of the Plagiarism policy for the institution and is considered cheating with penalties ranging from a grade of “zero” for the assignment to dismissal from the Institution.
The use of artificial intelligence and text generators is allowed in this course with proper attribution; use artificial intelligence as a tool, but do not use it to replace human intelligence. Trust me, it shows.
“You cannot do a kindness too soon, for you never know how soon it will be too late”
- Ralph Waldo Emerson
Because there are a few weeks between modules, this allows ample time to complete your assignments. Therefore, Late Assignments will not be allowed. This is because detailed solutions to the assignments will be made available after the due date and it’s just not fair for the other students who completed the assignments on time.
“Great discoveries and improvements invariably involve the cooperation of many minds”
- Alexander Graham Bell
Below is how the discussion topics in this course will be assessed.
| Criteria | Exemplary Rating |
Effective Rating |
Minimal Rating |
Unsatisfactory Rating |
Maximum Weight |
|---|---|---|---|---|---|
| Quality of Initial Post |
35 Points The student submits a post that demonstrates a thorough understanding of relevant concepts and correlates to course material. All components of the discussion prompt are addressed. |
20 Points The student submits a post that demonstrates general comprehension of relevant concepts and correlates to course material. All components of the discussion prompt are addressed. |
10 Points The student submits a post that reflects little evidence of general comprehension of course concepts. |
0 Points The student does not post, or the answer does not reflect evidence of comprehension of course concepts. There is no evidence of quality in the post. |
35% |
| Response to Peers | 30 Points Responses to at least 2 peers are well developed and relevant. Multiple points from peers are clearly built upon/refuted in postings. |
15 Points Responses to several peers offer some analysis but may need to offer additional information. At least one point from multiple peers was clearly built upon/refuted in postings. |
5 Points The student responds to only one or more points, from only one peer and vaguely builds upon/refutes in postings. |
0 Points The student does not respond to posts. No evidence that any other postings have been read. |
30% |
| Timeliness & Frequency of Engagement | 20 Points The student submits an initial post on time and is active on the discussion board at least three days out of the week. |
10 Points The student submits the initial post on time and is active on the discussion board at least two days out of the week. |
5 Points The student submits the initial post late and is active on the discussion board 1 day out of the week. |
0 Points The student does not post by the module end date. |
20 % |
| Writing Mechanics | 15 Points Writing is clear with no grammatical errors and maintains an academic structure; adheres to APA or MLA format (or other in certain circumstances) for citations and references. |
10 Points Writing may need some improvement; some sentences are confusing or contain a few grammatical errors. Some small errors in MLA or APA (or other where applicable) documentation may be present. |
5 Points Writing may contain a moderate number of grammatical errors and/or lack clarity. APA or MLA (or other where applicable) documentation may have been minimally attempted. There are no examples of overt plagiarism. |
0 Points Writing may be plagiarized (ex: citations, quotation marks, and/or reference entries are missing where they are needed). Writing may contain an unacceptable pattern of sentence-level errors with or without plagiarism, and it may lack an academic structure. |
15% |
“The ones who are crazy enough to think they can change the world are the ones who do.”
- Steve Jobs
P.S. That’s why I became a teacher
| Criteria | Exemplary Rating |
Moderate Rating |
Needs Improvement |
Maximum Weight |
|---|---|---|---|---|
| Creativity | 10 Points The student utilized at least 3 methods of artistic ability such as music, visual graphics, to keep and enhance the audience’s attention. |
5 Points The student utilized at least 1 method of artistic ability such as music, visual graphics, to keep and enhance the audience’s attention. |
0 Points The student utilized 0 methods of artistic ability such as music, visual graphics, to keep and enhance the audience’s attention. |
10% |
| Instructional Methodology |
20 Points The student used a wide assortment of differentiated instruction techniques to enhance the learning process |
10 Points The student used limited differentiated instruction to enhance the learning process. Instead, most of the demonstration was listened to, and not visualized. |
0 Points The student used no variation in instructional delivery. |
20% |
| Knowledge of Topic |
30 Points The student demonstrated confidence in the topic at hand. Little to no mistakes were made during the presentation. The student used different tones in their voice to capture the audience’s attention and demonstrated enthusiasm. |
15 Points The student demonstrated lack of knowledge in 1 or more areas of the topic. The presence of “Ums” and “Uhs” were prevalent during the presentation. |
0 Points The student demonstrated little to no knowledge of the topic at hand. The student also lacked enthusiasm in the topic. |
30% |
| Peer Review (Instructor) |
20 Points The student reviewed their peers and provided constructive feedback. |
10 Points The student missed 1 or more peer reviews and/or the feedback provided was not constructive. |
0 Points The student did not submit a peer review and/or constructive feedback was not provided |
20% |
| Peer Review (Students) |
20 Points The feedback provided by the students was largely positive. |
10 Points The feedback provided by the students was a mixture of positive and improvement measures. |
0 Points The majority (at least 75%) of the feedback is regarded as methodologies for improvement. Little to no positive feedback is provided. |
20% |
“The Quality of a Leader is reflected in the expectations they set for themselves”
- Anonymous
The following statements come from the American Mathematical Society Journal in 1996 by Dr. Steven Zucker with a few experiences of my own.
The underlying premise, whose truth is very easy to demonstrate, is that most students who are admitted to a college were being taught either at below their level, or they were simply given the grade to move on and graduate. The intent for any college is to reduce the time it takes for the student to appreciate the workings of mathematics and to help him/her adjust to the demands of working up to the level of college mathematics. Thus, there are a few things that ought to be pointed out.
You are no longer in High School. The clear majority of you, not having done so already, will have to discard high school notions of teaching and learning and replace them by college-level notions. Hopefully sooner than later. College is designed to get you to think critically, not just regurgitate.
Fast-Paced Class. Expect to have the material covered at two to three times the pace of high school. Above that, we aim for greater command of the material, especially the ability to apply what you have learned to new situations.
Lecture Time. Lecture time is at a premium, so it must be used efficiently. It is your responsibility to learn the material. Most of this learning must take place outside the classroom. You should be willing to put in roughly two hours per week for each hour of class.
My Responsibility. It is my job, to primarily provide a framework, with some of the particulars, to guide you in doing your learning of the concepts and methods that comprise the material of this course. It is not my responsibility to give you the example problems of every scenario. It is your job to apply the techniques that we use in lecture to new situations. It is not to “program” you with isolated facts and problem types nor to monitor your progress.
Expectations: I expect that you know the pre-requisites for this course. If you feel uncomfortable with the pre-requisite material, it is up to you to review the material. Also, you are expected to read the E-book for comprehension. It gives a detailed account of the material of the course. It also contains many examples of problems that are worked out, and these should be used to supplement those you see in the lecture. The text is not a novel, so the reading must often be slow going and careful. However, there is a clear advantage that you can read it at your own pace. Use a pencil and paper to work the material and fill in any omitted steps.
Studying for Math Classes: Studies do show that students in any class, particularly math classes, should spend 3 times the class credit hour just studying the material outside of class. In other words, if a student is taking a 3 credit class, then they should spend at least 9 hours per week outside of the lecture just working on assignments and reviewing the material.
Utilizing AI: While AI is a great tool to use, I expect everyone to utilize it to their advantage. However, I strongly suggest that you do not let it replace your thinking and problem-solving skills. Many students will put in a problem and trust the answer that it produces.
By remaining in this course, you agree to the terms and conditions set forth by the syllabus content.
Online learning offers flexibility in course completion, but also involves some challenges beyond those experienced in a traditional class setting. Here are some things to keep in mind:
Time commitment. Online classes take as much time as regular on-campus classes. You need to set aside sufficient time for study. Plan to spend at least as much time working on the assignments and studying as you would with a traditional course. Note that some students report spending even more time for online classes than for traditional ones.
Self-motivated and independent learner. While online courses can offer more flexibility in scheduling, they require more self-discipline and independence than on-campus courses. Some students can find this uncomfortable and not suitable for their learning style. They may miss face-to-face interaction with an instructor and peers, which helps to keep them on track. In the online environment, you have to be able to start and to work on tasks on your own, without someone keeping you focused, and you have to be self-disciplined in order to follow the class schedule and meet deadlines.
Time Management. Log in frequently and develop study
schedules
Even though you may not have to “be” in class on some specific day and
time, you still have to follow the course schedule provided by your
instructor. Remember that online classes are not independent study
courses; you are still required to “show up” and participate
actively.
Since online courses are asynchronous, they will continue developing and
changing even if you are not online. You need to be online frequently
enough and log in at least three to four times per week in order to keep
up with the content flow, complete assignments, follow discussions and
communicate with your classmates and instructor. Some courses may even
require you to log in every day.
Never wait until the last minute to complete your assignments. You may
have a technical problem or run out of time which will cause
frustration. One of the major challenges in online classes is
procrastination. Make sure to set aside specific time on a regular basis
to participate in your course. It is advised to schedule specific times
to log in and to study.
Computer Literacy You need to have a basic knowledge of
computer and Internet skills in order to be successful in an online
course. Here are some of the highlights (this list is not a complete
list)
Internet skills (connecting, accessing, using browsers) and ability to
perform online research using various search engines and library
databases.
Ability to use online communication tools, such as email (create, send,
receive, reply, print, send/receive attachments), discussion boards
(read, search, post, reply, follow threads), chats, and
messengers.
Strong Reading and Writing Skills. You need to have strong reading skills and be able to communicate effectively through writing. Most of the material in the online environment will come from your textbooks and written lectures, therefore strong reading and critical thinking skills are very important for success in an online course. Online students communicate through such text-based tools, as emails, discussion forums, chats and messaging. You need to feel comfortable expressing yourself in writing.
Active learner
Online students must be active learners, self-starters who are not shy or afraid to ask questions when they do not understand. Remember that you, not the instructor, must be in control of your learning process.
Since your instructor cannot see you, you need to “speak up” right away if you have problems and be as explicit as possible; otherwise there is no way others will know that something is wrong.
Remember that your instructor is not the only source of information. Most of the time you will be able to post your question in the discussion forum and your classmates will help you as well.
If you have technical difficulty, problems understanding course content or difficulty meeting the deadline, seek help right away via Tech Support or your instructor.
My mission is to prepare you for future coursework and the workforce by providing you, through instruction, the tools to think critically and apply your mathematical knowledge to real-world situations. I wish each and every one of you the best of luck in this course!
To keep up with important institutional dates, please see the academic calendar.
Feather River College Academic Calendar
FRC considers both cheating and plagiarism serious offenses. Penalties
are at the discretion of the Faculty member. Please refer to the FRC
catalog for the various types of academic dishonesty.
The document can be found by clicking the following link: Academic Integrity Policy
Students sanctioned for an academic integrity violation with an F in the
course before the add/drop or withdrawal period will not be permitted to
drop or withdraw from the course; the grade of F will stand. The Student
Code of Conduct is available in the FRC Catalog.
Students who receive Academic Sanctions for violating Academic Integrity
may appeal the sanction, only after the final Grade is awarded, using
the Grade Review and Appeal procedure detailed in the FRC catalog. (AP
4231)
Yes, I do check for academic integrity. Please understand that this is
not a standard statement.
The academic dishonesty process will be conducted as follows
Please refer to the FRC Catalog for further information. (AP 4231). The link for AP 4231 is located here: Grade Appeals and Grade Change Policy
If there is a concern about the class or the instructor, the following should occur in this order:
FRC is committed to creating an environment free of discrimination and promoting the safety of all individuals on campus.
The goal of a safe learning environment in this class is to prevent the occurrence of discrimination on the basis of sex, race, color, age, national origin (ethnicity), religion, sexual orientation, gender expression, disability, or veteran status and to prevent sexual harassment, sexual assault, or bullying.
A safe learning environment also means that a student should not fear retaliation if they express concerns or report a violation of this policy to the instructor.
In the event that you choose to write or speak about having survived sexualized violence, including rape, sexual assault, dating violence, domestic violence, or stalking and specify that this violence occurred while you were an FRC student, federal and state education laws require that, as your instructor, I notify the Chief Student Services Officer, Carlie McCarthy. She will contact you to let you know about accommodations and support services at FRC and possibilities for holding accountable the person who harmed you.
If you do not want the Chief Student Services Officer notified, instead of disclosing this information to your instructor, you can speak confidentially with the following people on campus and in the community. They can connect you with support services and discuss options for holding the perpetrator accountable.
Kelsie Foster, counselor, Ext. 234
Plumas County Intervention and Resource Center 530-283-5515 or 1-877-332-2754
Plumas District Hospital Emergency Room 530-283-7111
Plumas County Mental Health 530-283-6307
FRC recommends the phone application of My3 – available for free in the Apple App Store and Google Play. This app is a safety plan which links you to a network of three people (of your choice) for support and intervention should you have thoughts of suicide.
(Established and approved by the Council on Instruction: October 2012, Revised November 2015, July 2018, December 2018, July 2019.)
Now that you’ve read through the Course Syllabus,
Return to Canvas
Begin your assignments in Module 1
Brew some Coffee
Ace DiffyQ and Do Awesome Things!