Course overview

Choosing the correct course:

MATH1101 is a second course in the calculus of one variable intended for biology, computer science (BA), economics, management, and premedical students. It is open to others who are qualified and desire a more application-focused approach to calculus II at the core level. This course satisfies the core requirement for Mathematics.

Prerequisite:

• MATH1100 Calculus I or equivalent course (e.g., AP Calculus AB) in single-variable differential calculus, including knowledge of limits, derivatives, exponential, trigonometric, and logarithmic functions.

Further course placement information:

• Students contemplating majors in Chemistry, Computer Science/B.S., Environmental Geosciences, Geological Sciences, Mathematics, or Physics should enroll in MATH1103 unless you have specifically discussed placement in this class with your major program director or major advisor.

• MATH1101 is not open to students who have completed MATH1103.

• For more information about choosing the appropriate calculus course for your needs: [click here].

Course format and schedule:

• See the course calendar for a complete schedule and list of topics

• There are two midterm exams and one final exam.

  • Midterm 1 is on 7.20 (W) and Midterm 2 is on 8.1 (M).

  • The final exam is on 8.10 (W). The final exam is not cumulative.

Recommended course materials:

We will mainly use lecture notes and handouts. The textbooks below are not required. However, if you want to read one of these but you are not able to find an affordable copy, please let me know. There are plenty lying around in the math department.

• Stewart, James. Single Variable Calculus: Early Transcendentals, 9th Edition. Cengage learning.

• Stewart and Clegg. Brief Applied Calculus. Cengage learning.

Technology we will use:

• Email: for submitting homework problems

• Google drive: for checking homework feedbacks, and checking current accumulated grade.

• Discord: for collaborating, after-hour hw questions, and socializing.

Course content and goals

Course content:

Why learn calculus? The mathematician Joseph Fourier (1768-1830) said “Mathematics compares the most diverse phenomena and discovers the secret analogies that unite them.” Calculus is full of these secret analogies. The idea of rates of change, accumulation, and approximation are everywhere, from population growth and decline, to price and demand in economics, to the probability an event will occur. Calculus gives a qualitative and quantitative way to describe these phenomena, through derivatives, integrals and limits.

In this course, we will focus on three key ideas of calculus: integrals, differential equations, and derivatives of multivariable functions. We will learn their definition and conceptual meaning, various computational approaches, and applications to other problems.

Specific topics includes:

• Integrals Definition, Fundamental Connection to Derivatives, Basic Techniques for Computation, and Improper Integrals (Stewart Chapter 5 Sections 1-5, Chapter 7 Section 8)

• Applications to Integrals Area, Accumulation, Mass, Probability and others (Stewart Chapter 6 Section 1, Chapter 8 Section 5, and supplements)

• Introduction to Differential Equations Definition, Solving Basic Equations, Analyzing Solutions Qualitatively for Long-term Behavior, Applications to Population Dynamics, et al. (Stewart Chapter 9 Sections 1-6, supplements)

• Introduction to Multivariable Functions & Derivatives Visualizing Functions of Multiple Variables, Partial Derivatives, Linear Approximation, Optimization, Applications to Economics, et al. (Stewart and Clegg Chapter 7 Sections 1-4, supplement)

Learning goals:

In addition to learning the skills and concepts above, you will have the chance to develop your math practices and learning strategies - tools for how you learn and do math. You can use and adapt these to your other courses and future careers, regardless of the field. The full list is below, but the short version of these can be summed up as:

Compute, use Concepts, Communicate about and Apply mathematics.

• Become more proficient in computations: including working with basic algebra, functions, derivative, integral, limits

• Become more proficient in key concepts: particularly that of integrals, derivatives, and linear approximation

• Make sense of and solve problems: Translate between verbal, graphical and analytic representations of math, and problem-solve (understand the problem, make and implement a plan, reflect on the answer)

• Apply Mathematics in Context: Use the tools of calculus and functions to analyze phenomena in different disciplines, such as economics and life sciences. Use unit analysis to make sense of models and computations in context.

• Communicate verbally and in writing: Be able to explain the reasoning and concepts (the “why" and “how") behind the computations and theorems you use, using words, graphs and notation.

• Collaborate productively with others: Learn how to work with peers on math problems, ask questions about others' ideas, and give feedback.

• Reflect and Ask Questions: Engage in strategic self-questioning, about how you learn, about the content and concepts, and about how math might connect to your wider world.

Resources to help you succeed

Student drop-in hours:

These are also known as office hours. I will be in my office Maloney 537 MW 4 - 5:30pm and you can drop by to ask any questions you have. If the time and place doesn't work for you, you can also ask for a meeting on zoom/discord.

Tips for success:

Be responsible for your learning! This is key to success in a college course. Here are some guidelines:

• Be There Actively participate in all the classes.

• Make it Daily You will do much better if you work the course almost every day (even if only for a short time) rather than if you try to do the homework right before the deadline. Learning math is much like learning to play an instrument, or training for a sport: you need to get on a schedule where you do it every day, not just once a week in a marathon session.

• Come to Student Drop-In Hours When you have questions, come see your instructor. Don't wait if you feel like you are struggling with the course or a topic.

• Work Alone and Work with Others Try starting homework on your own, then discuss problems with peers. Talking about math with others is one of the best ways to strengthen your learning and have fun in the process!

• Be Patient - Doing math can be hard Someone once said “Those who don’t think math is hard haven’t been doing math long enough.” Part of learning problem-solving skills is a lot of getting stuck and false starts. This doesn’t mean you’re doing anything wrong, but it helps to try again and talk it out. Don’t wait until the last minute to do homework, give yourself time to get stuck and ask for help.

• Be Communicative - We are here! Please don't hesitate to email/discord me! If you miss a class or an assignment deadline, find yourself generally falling behind, suffer or anticipate a personal crisis, or have general concerns about the class or your performance in it, we will do our best to find ways to help within the course policies. No problem is too small, since small problems tend to pile up quickly and are easier to address.

Start with these guidelines, and adjust as you find what works best for you to master the ideas of the course. Feel free to come talk to me if you have questions about strategies!

Grades and assignments:

This is probably the most exciting section of the whole syllabus. For this class, we are introducing a new grading scheme that gives you a lot of flexibility for your learning. In short, you are in control of how much percentage homework grades and exam grades contribute to the final grade, from 0% - 100% to 70% - 30%. Here is how it works:

Homework:

There are two types of homework problems, 5pt and 10pt. It will be graded on the following scale:

• 5pt question: 0 incomplete - 3 major mistake - 4 minor mistake - 5 correct

• 10pt question: 0 incomplete - 5 major mistake - 9 minor mistake - 10 correct

You are allowed to redo a problem until you get full points.

You can submit 700pt worth of homework max. If you submit more than 700pt, we will start to use the average grade for all of those problems. Every 10pt (after grading) is converted to 1% of final grade.

To make the choice (of problems to do) easier, each problem will be labelled with the topic we covered in class. I recommend that you try 2-3 problems for each topic.

There are no weekly deadlines for the homework problems and redos. However, I will stop collecting problems for each section of the material on the corresponding midterm/final day. (For example, I will stop collecting problems about integrals on July 20th 8am.)

You should email me the problems you have done, and I will email you back with feedbacks on the same day. I will also archive a copy in the google drive and update your grade in the spreadsheet.

Exams:

There are three exams about integrals, differential equations, and multivariable functions each. Each exam contributes 1/3 to your exam score of the course, which is 100 - 0.1* (# pts of hw problems you have attempted).

For the two midterms, there are in-class portion (50 min, closed-books) and take-home portion (~24 hours, open-notes). The take-home portion will due on 7.21 (Th) and 8.2 (Tu) 11:59pm, submitted through email.

All three exams are take-home (~24 hours, open notes).

The final exam will be in-class only and open notes. The final exam is not cumulative.

Policies and additional resources

Grace, Flexibility and Accomodations:

We recognize these continue to be challenging and fluctuating times. Depending on the Covid situation, we may need to change how we run class at different points, including

• Using laptops or tablet for class work, instead of paper

• Conducting class and tests remotely on Zoom

We will communicate via email should this become necessary.

If you have concerns about being able to successfully complete course work due to illness or personal stress or emergency, please reach out to your instructor asap. We will do our best to be reasonable with accomodations, and we may waive the usual level of documentation when excusing absences, extending deadlines, or providing make-ups. However, you are asked not to take advantage of this policy, in consideration for fellow students experiencing unusual and extraordinary hardship during this time. We reserve the right to request documentation through traditional sources, namely your dean’s office and University Health Service, in instances where students are perceived as taking advantage of lenient policies. Suspected instances of academic dishonesty will be reported per traditional standards.

Recording:

All recordings will be stored within the canvas site and will only be available to view by members of this course. Lecture notes will be available here.

Academic Integrity:

Any work with your name on it is presumed to be your own and not copied from another person, the internet, or a textbook. Copying solutions from either the textbook or another person and submitting them as your own is plagiarism and is an infringement of the Academic Integrity Policy. Any infringement of the Academic Integrity Policy is taken very seriously and reported to the dean. You can read more about the policy at www.bc.edu/integrity. If you have questions about what constitutes appropriate collaboration vs. plagiarism, contact your instructor or see Homework Collaboration above.

Confidentiality:

The Family Educational Rights and Privacy Act (FERPA) prohibits instructors from sharing any information about your grades, with the exception of specific instances. See www.ed.gov for complete details. In particular, educational information cannot be shared with a parent or guardian of a student attending a school beyond the high school level without explicit permission in writing from the student.

Disabilities:

If you are a student with a documented disability seeking reasonable accommodations in this course, please contact Kathy Dugan, 617-552-8093, dugganka@bc.edu, at the Connors Family Learning Center regarding learning disabilities and ADHD, or Rory Stein, 617-552-3470, steinr@bc.edu, in the Disability Services Office regarding all other types of disabilities, including temporary disabilities. Advance notice and appropriate documentation are required for accommodations. Students are responsible for arranging accommodations for each midterm and the final exam.

Respect in the Classroom:

A college classroom is a learning environment. Please silence all electronic devices during class and do not use them except as directed for coursework. You are expected to treat the instructor and your classmates with consideration and respect. This includes avoiding unrelated conversations once class has begun, raising your hand to ask questions, and keeping the instructor notified of anything that will disrupt your active participation in class.

This class requires you to work with other students. Because the contribution of ideas from each student is critical to the learning process, please make every effort to maintain an atmosphere where everyone feels comfortable sharing and responding to ideas. If behavior detracts from a safe and respectful environment for learning, please let your instructor know. Also, your instructor may reach out to you if any issues arise, so that we can continue to support a learning environment for all.

Inclusivity:

It is our intent that students from all diverse 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. It is also our intent to present materials and activities that are respectful of diversity: gender, sexuality, disability, age, socio-economic status, ethnicity, race, and culture. Your suggestions are encouraged and appreciated. Please let us know ways to improve the effectiveness of the course for you personally, or for other students or student groups.

With this in mind, we have listed below 4 foundational principles, defined by Fedrico Ardila, for building mathematical spaces that welcome and serve every interested participant:

Axiom 1. Mathematical potential is distributed equally among different groups, irrespective of geographic, demographic, and economic boundaries.

Axiom 2. Everyone can have joyful, meaningful, and empowering mathematical experiences.

Axiom 3. Mathematics is a powerful, malleable tool that can be shaped and used differently by various communities to serve their needs.

Axiom 4. Every student deserves to be treated with dignity and respect.

Additionally, you should have received a poll asking you to specify your name and personal gender pronoun. If you have a different name than what is on the class roster, please let us know. If you have any questions or concerns, please do not hesitate to contact us.

Mental Health and Wellness:

Life at college can get very complicated. Students sometimes feel overwhelmed, lost, experience anxiety or depression, struggle with relationship difficulties or diminished self- esteem. However, many of these issues can be effectively addressed with a little help. University Counseling Services (UCS) helps students cope with difficult emotions and life stressors. UCS is staffed by experienced, professional psychologists and counselors, who are attuned to the needs of college students. The services are free and completely confidential. Find out more at www.bc.edu/offices/counseling or by calling (617) 552-3310.

Title IX:

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, Boston College policies require that, as your instructors, we share this information with Melinda Stoops, Boston College’s Title IX Coordinator, though we are not required to share any of your personal information. Should you wish, Melinda can contact you to let you know about accommodations and support services at Boston College as well as options for holding accountable the person who harmed you. You are not required to speak with her.

If you do not want the Title IX Coordinator notified, instead of disclosing this information to us, you can speak confidentially with the following people on campus and in the community. They can connect you with support services and help explore your options now, or in the future.

• BC’s Sexual Assault Network, available 24/7 at 617-552-2211

• Women’s Center (Maloney 441) Care Team Drop-In Hours. The hours for the semester can be found at https://www.bc.edu/offices/wc/SANet/Find_Support.html.

• University Counseling Services at 617-552-3310

• Boston Area Rape Crisis Center (BARCC), available 24/7 at 800-841-8371

• Fenway Health, a LGBTQ+ focused care center, available at 617-927-6250

• RAINN, a free, confidential, national sexual assault hotline, available at 800-656-HOPE

If you are a survivor or someone concerned about a survivor and need immediate information on what to do, please go to https://www.bc.edu/offices/wc/SANet/Find_Support.html