Basic Info

Calculus I: Change Happens

Calculus II: Changes Accumulate

In Calculus I, one learns how to describe change. The derivative tells us the instantaneous rate of a function. For a line, the rate of change is simple: it's just the line's slope.

In Calculus II, we'll think about how changes accumulate. Given a rate of change over a period of time, how much total change has occurred. If the change rate is constant, the process is simple: the total change is the rate of change times the time. But what to do if the rate of change isn't constant? Under those circumstances, how might we determine the total change? In Calculus II we'll thoroughly answer these questions.

This is not a traditional Calculus II class! I have taught Calc II many times (14, to be exact). And I have been increasingly unhappy with the material in past versions of the class. The traditional topics taught in the traditional way are, at best, somewhat tedious and not current. At worst, a traditional Calculus II class teaches students to do things that computers can do for you, which ends up not only being unnecessary but actively obscures the key ideas of integral calculus. So I'm going to try something new, which I piloted the last time I taught the class. Here's some of what I'm thinking.

• I am convinced that coding up some of the ideas and procedures from integral calculus is a great way to gain a true conceptual understanding. So we'll learn some basic python as part of this class.
• The main goal of learning python is to use it to learn calculus. But, of course, programming is a super valuable skill that is used across the sciences, the social sciences, and basically everywhere. Programming is also super fun.
• Since this class will be small, I would like to do a lot more "hands-on" explorations and even less lecturing than I usually do.
• What sort of hands-on explorations? New this year: model rockets! We'll all build and launch model rockets. We'll then use flight data and the model rocket engine's thrust curves to analyze rates of change and accumulated changes. In this case, the accumulated change we're interested in is the height of the rocket.

Btw, this course meets the following degree requirements: QR and ES

Who/when/where

• Instructor: Dave Feldman
• Pronouns: he/him/his
• Meeting Times: Monday, Wednesday, 2:30 - 4:00; Thursday 4:10 - 5:30
• Location: Room 103, Center for Human Ecology
• Help Sessions: Help Session Schedule (updated frequently)
• Individual Meetings: By appointment
• Tutors: Noelle Stringer

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:

1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.
2. Everyone can have joyful, meaningful, and empowering math experiences.
3. Math is a powerful, malleable tool 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.

Course Information and Advice

Goals

1. Stay physically and mentally healthy and maintain intellectual and personal connection.
2. Experience the challenge, joy, and beauty of calculus and mathematics in general.
3. Improve your problem solving skills and mathematical confidence. Leave this course with an increased ability to do mathematics.
4. Gain a firm, grounded, enduring understanding of one of the big ideas of calculus: the integral.
5. Gain a good introduction to infinite sum and series.
6. Gain experience using some basic programming in python to help learn mathematics.
7. Have fun while learning a lot.

Structure and Pacing

1. We will kinda sorta cover chapters 5-10 in this textbook, but I won't be following the book closely at all. Thus, there is no required text for this class.
2. This class meets three times a week. There is not a dedicated lab time.
3. Some weeks, depending on scheduling and weather and life, class may only meet twice a week.

There will be several different parts to the course, each with a somewhat different feel:

• Accumulation of change. Here we'll learn different ways to calculate accumulated change. This will involve a good bit of programming. This part of the course will probably seem unrelated to Calculus I, and at times may seem a little bit more like a programming class than a math class. Toward the end of this part we'll introduce a construction known as the definite integral.
• The fundamental theorems of calculus. This part will be less computational and more mathematical. We'll see that the change accumulator (the definite integral) is closely related to the derivative from Calculus I. So at this point it should become clearer why this course is called Calculus II.
• Applications of integrals. Here we will learn several different ways that the definite integral gets used. We'll likely have seen some of the applications or contexts in the first part of the course, but now we'll be able to explore them in a little more depth.
• Sequences and series. This is a topic that is somewhat separate from the rest of the course. This part of the course will be a mix of programming and pencil-and-paper math. This part of the course will have a different feel to it. Most students find this a nice change of pace and a good way to end the course. (However, depending on how the rockets go, we might do some work with differential equations instead of sequences and series.)

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. The main work for this course will be weekly homework assignments. There will also be a final synthetic assignment toward the end of the term.
3. All work can be resubmitted without penalty up to (roughly) a few weeks after I return it to you.
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.

Other Thoughts

1. 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).
2. Since we'll be doing coding, you'll need to have a laptop or tablet to code on. All the work we'll will be in the cloud, so there's no need to download any software.
3. There is only one teaching assistant for this class. We'll have to figure out how to optimally schedule help sessions. Since this class is small, I'm confident that we'll be able to figure things out.
4. I would also encourage you to schedule some group work times without me.
5. You will probably also need to schedule time outside of class to work on model rockets and also some other explorations/challenges.
6. Since most of this course is non-traditional, I would encourage you to not consult other calculus references, as doing so may be confusing. (There are some exceptions to this, which I'll mention as the course progresses.)

Help Sessions

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. 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.

What your Evaluation is Based on

Your evaluation will be based on your performance on homework assignments. 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.

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'll spend 2 hours reading and preparing for class and 8.5 hours attending help sessions and completing assignments.

Schedule

Important Links

Rocket Resources