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Calculus I

David P. Feldman

College of the Atlantic, Fall 2024

Basic Info

Calculus is the Mathematics of Change

This course covers a fairly standard set of differential calculus topics, including the definition and interpretations of the derivative, techniques of differentiation, and applications of derivatives.

This class meets the QR requirement. It does not meet the ES requirement.


Who/when/where


Textbook

We will more or less follow the first four chapters of this textbook. There is no need to buy a copy. I have old copies of the book that you use if you want. (Btw, while calculus is the mathematics of change, calculus itself hasn't changed in a century or more. So there is no need to work with the most current version of a calculus text.)


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 fourteenth time teaching this course, so I have a pretty good sense of how it will go. There are four parts to this class (corresponding to the first four chapters in the textbook), each with a distinct feel:

  1. Review of functions. This may seem both too slow and too fast at the same time. The last week of this part of the class is always difficult. Experience has shown, however, that the review of functions is definitely worth it. It is essential for the rest of the course.
  2. Introduction to the derivative. Here we will learn what the derivative is and what it means. This is more conceptual and sometimes seems odd to those used to less conceptual and more algebraic ways of thinking about math.
  3. Techniques of differentiation. Having learned what the derivative is, we now learn lots of short cuts to calculate it. This part of the class is the most traditional, in that you'll learn some formulas and techniques, and then do lots of practice of those techniques.
  4. Applications of derivatives. Here we will learn several different ways derivatives get used. This is the most applied part of the course. It is somewhat more difficult, but most students find it the most interesting, too, and a good way to end the class.

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.


Stuff about Homework (and other Assignments)

  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. You can always re-submit work without penalty.
  8. 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.
  9. In addition to weekly homework, there will be a few larger, synthetic, and hopefully creative and fun assignments. There may also be one or two short, un-timed, open-notes exam-like assignments.
  10. 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).


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.


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.


What your Evaluation is Based on

Your evaluation will be based on your performance on homework assignments (approx 70%) and your lab assignments and exam-like assignments (approx 30%). 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.


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 Ken Hill or Associate Dean Kourtney Collum.


Gender-based discrimination: Title IX

COA is dedicated to establishing and maintaining a safe and inclusive campus where all community members have equal access to COA’s educational and employment opportunities. We strive to promote an environment of respect, safety, and well-being and will not tolerate gender-based or sexual discrimination nor sexual harassment of any kind.

As a faculty member, I am considered a “responsible employee” and am required to share any disclosures of sexual or gender-based misconduct with the Title IX Coordinator. This includes disclosures of experiences that happened before an individual’s time at COA. This is to ensure that all community members who have experienced sexual misconduct receive support, options, and information about their rights and resources. Community members are not obligated to respond to this outreach, and this will not generate a report to law enforcement.

For more information regarding Title IX, our institutional policy, and to access helpful resources, visit COA’s Title IX website: https://www.coa.edu/human-resources/title-ix.

If you have any questions or want to explore support and assistance, please contact COA’s Title IX Coordinator, Puranjot Kaur, at pkaur@coa.edu. Speaking to the Title IX Coordinator does not automatically initiate a college resolution. Instead, much of her work is around providing supportive measures to ensure you can continue to engage in COA’s programs and activities.

Note on Pregnancy and Related Conditions:

Title IX prohibits discrimination based on sex in education programs and activities. This prohibition on discrimination extends to pregnancy and related conditions. Pregnancy and related conditions encompass pregnancy, childbirth, miscarriage, termination of pregnancy, false pregnancy, lactation, or recovery from any of these conditions.

Students experiencing pregnancy or related conditions may voluntarily initiate contact with the Title IX Coordinator to request reasonable adjustments available under Title IX. Reasonable adjustments may include but are not limited to: excusing student absences; allowing students to make up missed work; opportunities to move around during class; additional breaks; missing some or all of a class session to nurse or pump, and to have the opportunity to make up any work missed. Information on lactation space on campus can be found here: http://www.coa.edu/human-resources/title-ix/support-resources/lactation-space.

Students who believe they have been subject to discrimination because of pregnancy or related condition status may file a formal complaint with the Title IX Coordinator. If you are a pregnant or parenting student, and you are in need of any adjustments. please let me know at your earliest convenience.


Statements about Academic Honesty and Hours of Academic Engagement


Schedule

Important Links

Week 00

Thursday, September 12, 2024

  • Introductions.
  • Handouts: None


Week 01

Class: Monday, September 16, 2024

  • Introductions. Different ways of thinking of Functions. Linear Functions.
  • Handouts: [Linear Functions]


Lab: Monday, September 16, 2024

  • Exponential Functions. Introduction to Field Guide to Functions.
  • Handout:


Class: Thursday, September 19, 2024


Assignment: Friday, September 20, 2024


Week 02

Class: Monday, September 23, 2024


Lab: Monday, September 23, 2024


Assignment: Friday, September 27, 2024


Week 03

Class: Monday, September 30, 2024


Lab: Monday, September 30, 2024


Assignment: Friday, October 4, 2024


Week 04

Class: Monday, October 7, 2024


Lab: Monday, October 7, 2024


Assignment: Friday, October 11, 2024

Assignment: Friday, October 11, 2024


Week 05

Class: Monday, October 14, 2024


Lab: Monday, October 14, 2024

  • The derivative function. Interpreting derivatives. The second derivative.
  • Handout: [Lab 05 handout]


Assignment: Friday, October 18, 2024


Week 06

Class: Monday, October 21, 2024


Lab: Monday, October 21, 2024


Assignment: Friday, October 25, 2024


Week 07

Class: Monday, October 28, 2024


Lab: Monday, October 28, 2024


Class: Thursday, October 31, 2024

  • No Class! Faculty retreat.



Week 08

Class: Monday, November 04, 2024


Lab: Monday, November 04, 2024

  • Work on this week's (or last week's) homework.


Class: Thursday, November 9, 2024

  • Optimization!
  • Handout: tba


Assignment: Friday, November 8, 2024



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. 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.