Math 103

Calculus I

First semester of the standard 3-semester calculus sequence 103/104/201. Every spring about half of the students from this course continue the sequence with 104.

Topics: limits, continuity, definition of derivative, standard differentiation formulas, implicit differentiation, applications of the derivative (related rates, optimization, curve-sketching), linearization, antiderivatives, L'Hôpital's Rule, the definite integral, Fundamental Theorem of Calculus, area between curves, integration by substitution.

Classes: meet 3 times per week, for 50 minutes. Generally offered MWF at 9, 10, 11 and 12:30 in the Fall semester only. The course is organized into small precepts of 20 to 30 students. There is one course head who coordinates with all the instructors to write the exams. All students have the same homework assignments and take the same midterm and final exam. The midterm and final count for the bulk of your course grade, typically about 70%. These are graded by all the instructors together and one person grades the same question for all the students in the course. Typically there are small quizzes in precept, once a week or every other week. (Some semesters every section takes the same quizzes but in other semesters each preceptor writes his/her own quizzes.) Homework and quizzes typically count as about 30% of your grade.

Textbook: Thomas' Calculus, Early Transcendentals, Single Variable with Second-Order Differential Equations (Customized for Princeton University) by Thomas, Weir & Hass, Pearson: Addison-Wesley, (12th edition).


Who Takes This Course?

Placement and Prerequisites

General information about placement and contact information for the placement officer can be found on the Math Placement Page.

Sample Problems

Working problems from these sample exams can give you a good idea of the expectations and content in these courses as you think about which course is right for you. Just reading the questions or the solutions can be very misleading however. Try the problems yourself!

Once you have tried the problems, you can check your answers:
Midterm Exam Solutions, Final Exam Solutions.


  1. How much work is this course?
    • It requires a steady time commitment. We expect that the weekly problem sets will take at least 3 hours to complete. To do well on exams, you need to work a lot of extra problems from old exams. So all in all you should be ready to spend a minimum of 10 hours/week outside of class, on average.
  2. How hard is it to get an A in this class? I absolutely have to get an A!
    • Sigh. There are no guarantees and you won't get the full benefit of your four years at Princeton if you limit yourself to classes where you can be sure of an A. To answer the question, grades in the math classes are curved, so your grade depends on how your work compares to that of the other students in the class. Generally speaking, the top 25% of all the students in the class gets an A or an A-. The middle 45% gets some kind of B and the remaining 30% mostly get C's, but we do regularly give D's or F's if necessary.
  3. I have more questions that are not answered here. What should I do?
    • First check the general Math FAQ page for more information. (There is a whole section there on how Princeton's calculus courses work.) If you still have questions, representatives from the math department will be available at freshman registration.