Calculus I
MAT 1500
4 credits
Fall 2025
Meeting Times: Mondays and Thursdays, 10:30 - 12:10
Location: Natural Sciences 3001
Instructor: Professor Abdul-Quader (or just “Athar”)
Email: athar.abdulquader AT purchase DOT edu
Office Hours: Mondays and Thursdays, 9:15 - 10:15 NSB 3003
Course Description
Prerequisite: Precalculus The basic concepts of the differential and integral calculus. Focus is on the applicability of these topics to an array of problems. The first course in a three-semester series.
Learning Outcomes
In parentheses below, you can see how the course learning outcomes map to the Mathematics / CS Program Learning Outcomes.
Upon completion of this course, students should be able to…
- Understand the concept of a function, and how functions are used to relate quantitative variables (PLO 1, 2)
- Describe functions visually, verbally, algebraically, and numerically (PLO 1, 2)
- Find the limit of a function algebraically and graphically (PLO 2)
- Compute derivatives using several methods (PLO 2)
- Apply techniques of differential calculus to solve problems in several domains (PLO 1, 2)
- Learn the relationship between antiderivatives and definite integrals (PLO 2)
- Explain the importance of calculus in examining topics in current events or historical developments in mathematics (PLO 3, 4, 5)
This course also fulfills the Core: Mathematics general education requirements, whose learning outcomes are listed on the Core Curriculum Learning Outcomes website
Required Textbook
Calculus Volume 1 by Edwin Herman and Gilbert Strang. This textbook is available for free online.
Students who desire additional resources can look into other textbooks, but none of these are required:
- Stewart, Essential Calculus: Early Transcendentals (2nd edition). This is a standard (but pricey) textbook for introductory calculus
- Spivak, Calculus (4th edition). This book is for students who are more interested in the rigorous mathematical underpinnings of calculus. This book emphasizes proofs over applications. If you are interested in higher mathematics, this might be worth looking into!
- Courant and John, Introduction to Calculus and Analysis I. An alternative to the Spivak book, it also is good for students who are interested in higher math.
Required Software
For some written homework assignments, students will need to use either a scanner app or a scanner to create a single PDF of all of their work and upload the work to BrightSpace. There are several good scanner apps available for Android and iOS devices, including CamScanner, Genius Scan, Adobe Scan and Microsoft Lens.
DeltaMath Online Homework
We will be using the free website DeltaMath for online homework. To access this software, you can create a free student account using this link. If the above link does not work, use the following steps:
- Go to www.deltamath.com
- Click “For students” and then “Register”.
- Enter Teacher Code 357935.
- Select MAT 1500 Calculus 1 Fall 2025 for “Class” and register using your purchase.edu email address please!
Grading Rubric
- 30% Homework and quizzes
- Note: This includes online homework, written homework, and quizzes
- 5% Classwork and participation
- This includes working on problems in small groups and, at times, presenting them on the board
- 10% Problem Presentations (2 short explanations of a homework / exam / other challenging problem, done in class)
- 20% Mid-semester exams (3 exams during the semester)
- 25% Final Exam
- 10% Final Paper
- 2% Topic statement
- 4% Initial research notes / outline
- 4% First draft
- 5% Final paper
Calculator Policy
A graphing calculator is required for this course. You are welcome to use online calculators like Desmos on homework assignments. For exams, I recommend the TI-84+ CE or the Casio fx-9750GIII. Unless otherwise specified, calculators are allowed for all assignments, including exams and quizzes.
Attendance
I understand that there may be times you miss a class due to emergencies, illnesses, and other reasons. For this reason, I post the lecture notes online and on BrightSpace. If you miss a class, be sure to submit any work that was due that day, find out what work you missed, and catch yourself up. You can use my office hours and the tutoring center to help catch you up.
Late Homework Policy
Mathematics is extremely cumulative, and so it is important to stay on top of your work when it is assigned. If you miss a class or fall behind, you still need to stay on top of the work that was covered. Do your best to stay current with the work, using all the resources at your disposal to help you.
If, due to emergencies or illnesses, you require some flexibility, you can reach out to me and we can discuss what you can do to make things up. However, if you fall behind on work and submit work late, I will have less time to actually look at it, grade it and provide meaningful feedback. If work is submitted too late, I reserve the right to simply give it a zero and move on if I do not have time to look at it.
Collaboration Policy
You are encouraged to discuss homework assignments and projects with other students. You must complete the assignment on your own, however. There is a clear difference between copying someone else’s work and discussing a problem with another person. The latter is encouraged. Plagiarising another student’s work can lead to academic sanctions as per Purchase College’s Academic Integrity Policy.
Office of Disabilities
It is my goal that this class be an accessible and welcoming experience for all students, including those with disabilities. You are welcome to talk to me at any point in the semester about course design concerns, but it is always best if we can talk as soon as possible about the need for any modifications. The Office of Disability Resources collaborates directly with students who identify documented disabilities to create accommodation plans, including testing accommodations, in order for students to access course content and validly demonstrate learning. For those students who may require accommodations, please call or email the Office of Disability Resources, (914) 251-6035, odr@purchase.edu.
Tutoring
Tutoring for this course is available from the Einstein Corner. Students can make appointments via the Starfish platform. More information here.
Wellness and Mental Health
Purchase College has many resources to support our students’ wellness and mental health. Please take a look at the Health and Wellness website for more information. In particular, check the Counseling Center’s website to learn about the various services that the Counseling Center has to offer, including remote counseling, emergency resources, hotlines, and referrals. Take care of your mental health!
Course Outline (Tentative)
| Week | Topics | Readings |
|---|---|---|
| 1 | Review of functions, intro to calculus | 1.1 - 1.5 |
| 2 | Limits | 2.1 - 2.3 |
| 3 | Limits and continuity | 2.4 - 2.5 |
| 4 | Basic derivatives, derivative rules | 3.1 - 3.4 |
| 5 | Review, Exam 1 | |
| 6 | Quotient rule, trig derivatives, chain rule, | 3.3, 3.5, 3.6, 3.8 |
| 7 | Implicit differentiation Exponential and Logarithmic functions, related rates | 3.9, 4.1 |
| 8 | More applications of derivatives | 4.1 - 4.5 |
| 9 | Exam 2; More applications, limits at infinity | Exam 2; 4.6 - 4.8 |
| 10 | Antiderivatives, areas | 4.10, 5.1 |
| 11 | Definite integrals and the fundamental theorem of calculus | 5.2 - 5.3 |
| 12 | Evaluating integrals, substitution | 5.4 - 5.5 |
| 13 | Exam 3, Applications of integrals | Exam 3; online resources |
| 14 | Review / overflow | |
| 15 | Review |
This is very much subject to change.