Office Hours: TBD
Email:pbonvent@holycross.edu
TA/Grader: Max Watson
Office Hours: TBD
Online. Classes will be conducted on Zoom, with some use of internet tools, such as Google Docs, Jamboards, and Canvas.
Multivariable Calculus: Concepts and Contexts, 4th edition (Enhanced) by James Stewart.
Warning: this is NOT the same as Multivariable Calculus: Early Transcendentals ALSO by James Stewart.
You will need access to WebAssign, the online homework system. This comes bundled with the physical book from the College bookstore, but can also be purchased entirely electronically on the WebAssign website (and comes with an digital version of the text).
Prerequisites: Math 134, Math 136, or a score of 4 or 5 on the AP Calculus BC Exam.
For more information, see the
Holy Cross Math Department website.
In the first year of calculus, you primarily studied functions with a real number as an input and a real number as an output. In multivariable calculus, you will study functions whose input and/or output is not a number, but is a point or vector in a two-, three-, or higher-dimensional space. The goal of the semester is to learn how to represent these functions graphically, what their applications are, and how calculus applies to these functions. We'll study both differentiation and integration on these classes of functions. Finally, we will study the connections between differentiation and integration, which look like higher-dimensional versions of the Fundamental Theorem of Calculus
In particular, during the semester you will learn about four new types of functions, and understand the application and interpretation of the techniques of calculus to them:
Research shows that people learn mathematics best when they are actively participating. In other words, you learn by doing, not by watching. This course and the book we are using are designed for a classroom which does not necessarily follow a traditional lecture format. To that end, class time will not be entirely devoted lecturing, and instead you will often spend a good amount of class time working on problems yourself, either individually or in groups. Moreover, certain days will be devoted in full to working collaboratively on small group "Lab Projects".
You will be expected to read a section in the book before it is discussed in class. Lectures are intended to highlight aspects of the text, not to replace it.
In this course you will learn a number of useful formulas, though their mastery is not the primary purpose of calculus any more than correct spelling is the primary purpose of literature. Our goal is to have you learn how to understand multi-variable calculus conceptually so you can build your own approaches to solving practical problems.
While working in groups:
The only effective way to learn Calculus is to practice. Besides working on problems in every class, you will have assignments and assessments in this course to enhance your skills and understanding.
Late assignments will not be accepted. However, only the 10 best scores of each type (WebAssign, Written, Quiz) will count towards your final grade.
Grades will be assigned based on the following scheme:
Participation — 20%
WebAssign — 15%
Written Homework — 15%
Quizzes — 20%
Exams — 30% (10% each)
I know this is a weird and difficult time for us all. I expect myself to work hard to make this class effective and flexible, and I expect you to do the same.
You are expected to complete your assignments, come to class on time and ready to participate and engage with the material and your fellow classmates.
Additionally, you are responsible for announcements made in class, as well as any emails sent to your UK email account or announcements on the course website.
Attendance is required. That being said, I expect there may be times where you are not able to make it to class, for a potential variety of health or personal reasons. If you must miss class, due to an illness or other pressing circumstance, please let me know as soon possible. I will not ask for medical documentation, and naturally the Class Deans are not going to be able to provide excused absences. Instead, I will trust your judgement and voice in these matters, and expect that you will take ownership of this trust and act responsibly.
As listed above, participation is 20 percent of your grade this semester. That includes in-class and lab project work and engagement, as well as attendance. Your energy into our class time together is essential to the effectiveness of this course, for you an your classmates.
You may have considerations that will prevent you from keeping your camera on during our synchronous meetings, including internet speed or access issues, family responsibilities, or personal discomfort, so you may absolutely leave your camera off if you want or need to do so. To the extent that you are comfortable and able to turn your camera on, though, please feel free to do so (and be mindful of what's within your camera's view or which virtual background you're using!). This will help us to create a sense of connection and community in our class and encourage engagement with and trust in one another.
Please try, however, to mute your microphone unless you are actively speaking or would like to offer a thought or question. This is to ensure that we give due focus to whoever is speaking and to avoid being distracted by unintended background noise.
Recording of the class sessions is not allowed, except with the explicit written permission by me, as part of an accommodation through the Office of Accessibility Services.
The College of Holy Cross (here) and the Department of Mathematics and Computer Science (here) both have policies on Academic Integrity. Please read these in full. By taking this class, you assume responsibility towards following this policy.
Mathematics is an inherently collaborative and social activity. On all of the homework assignments, you are allowed to --- in fact, encouraged --- to work together. However, when you write up your solutions, this should be done independently, and in your own words. Thus it is your own language and your own work. If you are wondering if you crossed the line, ask yourself: "Could I start over and redo this on my own, and would it basically look like this?" If not, then you are submitting someone else's work (plagiarism). Copying homework solutions from the internet also constitutes plagiarism. Plagiarism violates both the Holy Cross and the Math/CS Department policy on Academic Integrity, and will not be tolerated.
Quizzes are not open-book, but exams are. For both assessments, you are not allowed to work together, nor use the internet or other human or non-human resources.
The intention of the homework in this class is twofold: first, to have you practice the skills we learned in class, and get comfortable using the math technology we develop; and second, to apply those skills to new problems and different situations. We will not cover every type of problem that is on the WebAssign or Written Homework in lecture, and that is by design. Adapting your knowledge to new scenarios is a valuable asset. Being able to effectively use the resources available to you --- office hours, the textbook, your fellow students --- will be key to your success in this class. Part of my role is to help foster these skills, in addition to teaching you math.
It is my job to provide all students with an accessible learning environment. Some aspects of this course, the assignments, the in-class activities, and the way the course is usually taught may be modified to facilitate your participation and progress. As soon as you make me aware of your needs, we can work with the Office of Accessibility Services to determine appropriate accommodations. Any information you provide is private and confidential, and will be treated as such.
It is my 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 the students bring to this class be viewed a a resource, strength and benefit. It is my intent to present materials and activities that are respectful of diversity: gender identity, sexuality, disability, age, socioeconomic status, ethnicity, race, nationality, religion, and culture. 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.