Introduction

“The book of the universe is written in the language of mathematics.” Galileo wrote this four hundred years ago, even before Newton and Leibniz discovered calculus. The statement is as valid today as ever: We use functions in all the sciences, and calculus allows us to analyze the functions and draw scientific conclusions.

Calculus II is a second semester calculus course for students who have previously been introduced to the basic ideas of differential and integral calculus. Over the semester we will study three (related) topics, topics that form a central part of the language of modern science:

applications and methods of integration,
infinite series and the representation of functions by power series, and
parametric curves in the plane.

The material we take up in this course has applications in physics, chemistry, biology, environmental science, astronomy, economics, statistics, and just about everything else. We want you to leave the course not only with computational ability, but with the ability to use these notions in their natural scientific contexts, and with an appreciation of their mathematical beauty and power.

Course content and list of topics

Textbook

The course will closely follow the textbook Essential Calculus, Early Transcendentals, Second Edition, by James Stewart.

The course also requires a subscription to Cengage WebAssign for our particular textbook. Please note that the WebAssign subscription includes digital access to the textbook.

Topics covered

Below is a list of topics that will be covered and their respective sections.

5.5 - Change of Variables

6.1 - Integration by Parts

6.2 - Trig Substitution

6.3 - Partial Fractions

6.5 - Approximations

6.6 - Improper Integrals

7.1 - Areas

7.2 - Volumes - Disks

7.3 - Volumes - Shells

7.4 - Arc Length

7.7 - Differential Equations

8.1 - Sequences

8.2 - Series

8.3 - Tests for Series Convergence

8.4 - Tests for Series Convergence

8.5 - Power Series

8.6 - Functions to Power Series

8.7 - Taylor Series

8.8 - Applications of Taylor Series

9.1 - Parametric Curves

9.2 - Calculus with Parametric Curves

9.3 - Polar Coordinates

9.4 - Calculus with Polar curves

Course work

Students in this course will:

do online homework (via WebAssign)
do problem sets (submit via Gradescope)
take quizzes
take 2 midterm exams, and
take a 1 final exam.

Online HW (via WebAssign)

WebAssign is an online homework platform and can be accessed via Brightspace. WebAssign requires a subscription. The due dates of each assignment will be indicated within WebAssign. The purpose of WebAssign HW is to allow students to get immediate feedback on their work. WebAssign also allows students to see more questions they don't get to see in class or during exams.

Problem Sets

Problem sets will be posted on Brightspace and/or Gradescope, and the due dates of each assignment will be indicated. These problems typically involve critical thinking, and full solutions must be presented. The purpose of the problem sets is to challenge students into applying fundamental concepts learned in class into new or unique situations they may not have seen before. In addition, the problem sets require students to present worked solutions in a clear, logical manner.

Quizzes

Quizzes are formative assessments to test students’ understanding of the material. The purpose of quizzes is to ensure students are understanding the material currently being covered and discussed in class and to ensure they are involved throughout the semester. In addition, the quizzes will allow students to experience an exam-like environment.

Midterms and Final Exams

Two midterm exams will be given during the semester. The midterms will be summative assessments and comprehensive of the course material taught until that point. A final exam will be given at the end of the semester that assesses students’ understanding of all the course material. The purpose of the exams is to test students' understanding of the course material in a summative, holistic approach. Some problems may involve multiple concepts.

Extra help and tutoring

In addition to your professor’s office hours, the University provides a few options for extra help.

The University Learning Center offers a variety of services, including drop-in tutoring and review sessions, all done via Zoom. More information and schedules can be found here: https://www.nyu.edu/students/academic-services/undergraduate-advisement/academic-resource-center/tutoring-and-learning.html

The Department of Mathematics also offers drop-in tutoring, all done via Zoom. More information and schedule can be found here: https://math.nyu.edu/dynamic/undergrad/tutoring/

Miscellaneous

Student Accessibility

New York University is committed to providing equal educational opportunity and participation for students with disabilities or accessibility concerns. It is the University's policy that no qualified student with a disability or accessibility concern be excluded from participating in any University program or activity, denied the benefits of any University program or activity, or otherwise subjected to discrimination with regard to any University program or activity. The Henry and Lucy Moses Center for Students Accessibility (CSA) determines qualified disability status and assists students in obtaining appropriate accommodations and services. CSA operates according to an Independent Living Philosophy and strives in its policies and practices to empower each student to become as independent as possible. Their services are designed to encourage independence, backed by a strong system of support. Any student who needs a reasonable accommodation based on a qualified disability or accessibility issue is required to register with the CSA for assistance.

Religious Observations

NYU’s Calendar Policy on Religious Holidays states that members of any religious group may, without penalty, absent themselves from classes when required in compliance with their religious obligations. You must notify me in advance of religious holidays or observances that might coincide with exams, assignments, or class times to schedule mutually acceptable alternatives. Students may also contact religiousaccommodations@nyu.edu for assistance.

Diversity, Equity, and Inclusion

As an instructor, I will strive to create a safe, respectful, and inclusive environment for all students regardless of their identity. I recognize and value diversity inside and outside of the classroom, and recognize that each student has a unique contribution to make and brings with them different strengths and weaknesses. I welcome your ideas for how to promote a better understanding and deeper learning in this class as a community. Please feel free to ask questions, to participate in discussions, and to suggest new approaches to the class content. Please also feel welcome to raise any issue you may have in class or outside of class, including reporting incidents of bias or discrimination, whether intentional or unintentional, either to me, to your advisor(s)/mentor(s), or by using the NYU Bias Response Line: https://www.nyu.edu/about/policies-guidelines-compliance/equal-opportunity/bias-response.htm.