Basic Info

Differential Equations: Official Course Description

Differential equations are an application of calculus used to model a wide variety of physical and natural phenomena. The rate at which a cup of coffee cools, populations of predators and prey in ecosystems, the spread of disease, and the behavior of electric circuits, are all examples of systems that have been described with differential equations. This course is an introduction to ordinary differential equations, intended for students who have completed a single-variable calculus course. The course covers a variety of techniques for solving and understanding differential equations, including numerical and qualitative solution methods. Students will learn to solve and analyze differential equations using the python programming language. Students will also gain experience formulating mathematical models using differential equations. To do so, we will discuss general modeling principles and also consider several case studies. In addition to learning the mathematics of differential equations, a central goal of this course is to gain skills necessary for research in the mathematical, natural, and social sciences. This includes conceptualizing and framing a research question, conducing a literature review, giving a research presentation, and writing up results in a style appropriate for publication. Evaluation will be based on class participation, bi-weekly problem sets, and a term-long project culminating in a presentation and short research paper. Some computer work will be required, but no computer experience is necessary. Level: Intermediate. Prerequisites: Calculus II or the equivalent or permission of instructor. Lab Fee: none. Meets the following degree requirements: ES QR

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Who/when/where

• Instructor: Dave Feldman
• Pronouns: he/him/his
• Meeting Times: Monday, Wednesday, Thursday: 2:35 - 4:00
• Location: Room 103, Center for Human Ecology
• Help Sessions: Help Session Schedule (updated frequently)
• Individual Meetings: By appointment
• Tutors: None

Axioms

In mathematics, axioms are propositions that are assumed to be true. The mathematician Federico Ardila-Mantilla has written four axioms that guide the work he does in education and outreach. Federico's axioms resonate strongly with me. They are (slightly re-written to apply to physics as well as math):

1. Mathematical and physics potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
2. Everyone can have joyful, meaningful, and empowering math and physics experiences.
3. Math and physics are powerful, malleable tools that can be shaped and used differently by various communities to serve their needs.
4. Every student deserves to be treated with dignity and respect.

Community Agreement

Taking the above axioms as a starting point, let's think about what type of community we want to create this term. Here is a community agreement based on one written by Federico Ardila-Mantilla.

This course aims to offer a joyful, meaningful, and empowering experience to every participant; we will build that rich experience together by devoting our strongest available effort to the class. You will be challenged and supported. Please be prepared to take an active, critical, patient, creative, and generous role in your own learning and that of your classmates.

More Course Info and Advice

Structure and Pacing

This is my fifteenth time teaching this course, so I have a pretty good sense of how it will go. This class has several, overlapping parts:

1. During the first 1-2 weeks of the class we'll spend some time building community.
2. The first 1-4(ish) weeks we'll cover some core material and build up some skills. We'll cycle back to to key ideas frequently. This course is about building quantitative and analytical skills, and the only way to do this is through lots of practice. Weeks two-four may be a little challenging as you get your feet under you and (re)develop some skills.
3. The last half of the class you'll have a solid base of skills and so the mechanics of the homework will likely go more smoothly, while the physics and climate implications of what we cover will get more and more interesting.
4. At some point toward the middle of the course we'll take a little detour and learn some financial mathematics. You will likely find this more interesting than you think you're going to find it. Really.

There are two lab sections for the course. You should attend one lab session each week. Please attend the same lab each week if possible, but if not, it's not a big deal.

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Stuff about Homework

1. There will be an assignment due almost every Friday. It is essential that you do these assignments, as this is how one learns math, and also this is most of what your evaluation will be based on.
2. There will be two parts to almost every homework assignment:
   • Problems to be submitted on WeBWorK
   • Problems to be submitted on "paper" (a scanned pdf) on google classroom
3. WeBWorK is an online homework system. There are three reasons why I use WeBWorK:
   • You get instant feedback while doing the work, so you can learn right away from your mistakes. You can submit solutions many times until you get everything correct.
   • Some problems are randomized so that you will all get slightly different versions of the questions. This means that collaborating with other students will be maximally effective, since you'll have to share solution methods and not just the final answer.
   • Since the problems are automatically marked, I can spend more time helping you and won't have to spend as much time grading.
4. If you need extra time for one or two of the homework assignments, it's not a big deal. But be mindful to not fall farther behind every week.
5. I do not expect all of the homework assignments to be easy; I don't expect you to be able to sit down and do them easily the first time. Don't let yourself get frustrated. I strongly suggest working with others and seeking help if you need it.
6. You are strongly encouraged to work together on homework. You can also consult me, class tutors, other faculty, friends, and family. However, the homework you hand in should represent your own understanding.
7. As I plan on sending out homework assignments and other information via email/google classroom, it is important that you check your email/classroom regularly.
8. You will want to have at your disposal a scientific calculator or phone/tablet app. I strongly suggest an actual calculator. You do not need a graphing calculator for this course (or, in my opinion, ever).

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What this Class Isn't

1. This course is not about the following things, although this course should help you do/think about the following things better and more richly.
   • Energy policy
   • Social impacts of energy technologies
   • Environmental impacts of energy technologies
   • Weatherproofing your house
   • Building your own wind turbine
   • Climate change and global warming
   • A physics class
2. There may be a temptation to delve too deep into particular technology to the point that we're swamped with facts and details. There is also a temptation to get bogged down in discussions about policy, ethics, and justice. We should collectively resist these temptations; there are a lot of important topics to learn about.
3. Many of the examples in this class are based on a US context. I will incorporate other contexts as I can, and will try to make clear differences between the US and elsewhere in terms of energy.

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Help Sessions

The Teaching Assistants and I will have a handful of help sessions every week. You are warmly invited and encouraged to attend these sessions. Help sessions are relaxed, informal, and hopefully fun. Things that happen at help sessions:

1. The TAs and/or I am around to offer help on the homework.
2. Some students do most of the homework while at a help session. They work through problems alone or with others, and find it comforting to know that help is immediately at hand if needed.
3. Others do the problems at home and come to the help session with specific questions.
4. Some students work in groups at help sessions, others work more or less alone.
5. Help sessions are also a chance to ask general questions about the course. Conversations also sometimes wander into other areas: politics, the state of the world, what's for dinner, what classes are offered next term, and so on.
6. Help sessions are a great way to meet other students in the class.
7. Often there will be coffee/tea and/or snacks.

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Individual Meetings

I am happy to meet with students one-on-one. The best way to set up an appointment is to send an email. There are lots of reasons why you might want to meet with me:

1. You have some in-depth questions that there isn't time to explore in a help session.
2. You have a question that you think is too basic or you're uncomfortable asking in a help session. (You shouldn't be uncomfortable, since, as the saying goes, there are no dumb questions! But I understand that you might be uncomfortable nevertheless.)
3. You want to explore possibilities for energy projects on campus or in the community.
4. You want to discuss some challenges you're facing in the class.
5. You want to talk about other classes in energy or physics, or internships, senior projects, etc.

Please don't hesitate to reach out if there's anything you want to discuss. You should also feel free to reach out to the TAs.

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What your Evaluation is Based on

Your evaluation will be based on your performance on homework assignments (approx 90%) and your contributions in lab sections (approx 10%). There will be weekly homework assignments and, towards the end of the course, some mini-case studies and projects. I think there is much to be said against grades; I believe they often interfere with genuine, reflective learning. But I am happy to assign grades if you wish. I do not have any quota of A's, B's, etc.

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Diversity, Inclusion, and Belonging

It is my intent that students from all backgrounds and perspectives be well served by this course, that students' learning needs be addressed both in and out of class, and that the diversity that students bring to this class be viewed as a resource, strength, and benefit. I aim to present materials and activities that are respectful of diversity: gender, sexuality, disability, age, religion, socioeconomic status, ethnicity, race, and culture.

Learning about diverse perspectives and identities is an ongoing process. I am always looking to learn more about power and privilege and the harmful effects of racism, sexism, homophobia, classism, and other forms of discrimination and oppression. Your suggestions are encouraged and appreciated. Please let me know ways to improve the effectiveness of the course for you personally, or for other students or student groups. If something was said or done in class (by anyone, including me) that made you feel uncomfortable, please let me know. You can also reach out to: Provost Kourtney Collum; Puranjot Kaur, Coordinator of the Office of Title IX and Civil Rights Compliance; or Maya Caines, Restorative Practices Team Coordinator.

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Gender-based discrimination: Title IX

COA is committed to fostering a safe, respectful, and inclusive campus where all community members have equal access to education and employment. We will not tolerate sexual harassment or gender-based discrimination of any kind.

As a faculty member, I am considered a "Responsible Employee." This means I am required to share any disclosures of sexual or gender-based misconduct with the Title IX Coordinator—even if the incident occurred before your time at COA. The purpose of this requirement is to ensure that anyone who has experienced sexual misconduct is offered support, information about their rights, and access to available resources. Please know that you are not required to respond to outreach, and a disclosure does not automatically result in a report to law enforcement.

For more information about Title IX, COA’s policies, and available resources, please visit: coa.edu/human-resources/title-ix.

If you would like to ask questions or explore support options, you are encouraged to contact COA's Title IX Coordinator, Puranjot Kaur, at pkaur@coa.edu. Speaking with the Title IX Coordinator does not automatically initiate a college resolution process. Much of her work focuses on providing supportive measures to help you continue to fully participate in COA's programs and activities.

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Statements about Academic Honesty and Hours of Academic Engagement

• I am required to remind you that: "By enrolling in an academic institution, a student is subscribing to common standards of academic honesty. Any cheating, plagiarism, falsifying or fabricating of data is a breach of such standards. A student must make it his or her responsibility to not use words or works of others without proper acknowledgment. Plagiarism is unacceptable and evidence of such activity is reported to the academic dean or his/her designee. Two violations of academic integrity are grounds for dismissal from the college. Students should request in-class discussions of such questions when complex issues of ethical scholarship arise."
• I am also required to say that: You should expect to spend 150 hours of academically engaged time on this course, or 15 hours per week. In addition to 4.5 hours per week in class or discussion section, in a typical week you will spend 2 hours reading and preparing for class and 8.5 hours attending help sessions and completing assignments.

Schedule

Important Links

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Week 01

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Week 02

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Week 03

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Week 04

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Week 05

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Week 06

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Week 07

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Week 08

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Week 9

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Week 10

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The building in which we gather for this class, and all of College of the Atlantic, is located on traditional lands of the Wabanaki people. The four Native American tribes in Maine today are the Maliseet, Micmac, Penobscot, and Passamaquoddy, collectively referred to as the Wabanaki. Although largely a technical class, we will touch upon questions of energy colonialism and imperialism. I believe it is important to acknowledge that our presence on this land entangles us in the web of colonialism, past and present. The future, however, is still unwritten.

In this class we will learn about non-fossil fuel sources of energy. Transitioning to a fossil fuel free society is essential to avoid catastrophic climate change. College of the Atlantic, and by extention all of us, historically and presently benefit from energy provided by inexpensive fossil fuel sources. Again, we are entangled with the system that we seek to replace.