Math 104

Calculus II (One Variable, Continued from 103)

Second semester of the 3-semester calculus sequence 103/104/201.

Topics: integration by substitution, integration by parts, partial fractions, trigonometric substitution, improper integrals, convergence tests for infinite series, alternating series, absolute convergence, power series, taylor series, complex numbers, first and second order differential equations, volume, length and surface area.

Classes: meet 3 times per week, for 50 minutes. Generally offered MWF at 9, 10, 11 and 12:30 in both Fall and Spring semesters. 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! For the moment, sample exams can be found at the 104 home page from Spring 2010.


  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. If I think 104 is too hard, what should I do?
    • Try an old final exam in 103. If you can do most of the problems with confidence, you should stay in 104. Otherwise, you may want to switch to 103 or 101 in the fall or to 102 in the spring.
  3. If I think 104 is too easy, what should I do?
    • We have designed 103/104 as a beginning calculus sequence. Entering 104 in the fall, you may well find that you are already somewhat familiar with the material taught in the first three weeks. Before switching up to a 200-level course, first try the sample final exam (above) and then check the answers. If you did not do quite well, you should stay in 104.
  4. I need both 103 and 104 for my major. After checking the math placement information, I think 104 is probably the right course for me, but I don't qualify for AP credit for MAT103. Do I have to take 103 or can I sign up for 104 instead?
    • First, be cautious. Students often underestimate the difficulty of 104 because many have seen some of the techniques taught in the first few weeks of the course. (The same can be said of 103, but most students consider 104 to be significantly harder than 103). Consider the information in the previous two questions as you think about your decision.
    • If you are really sure that you belong in 104, you can sign up for it. If you pass 104 in your freshman year, you will automatically receive AP credit for 103. Just be ready to re-consider and switch down to 103 early on if necessary.
  5. If I want to switch courses, what should I do?
    • Talk with your 104 teacher. You may also want to talk with the teacher in charge of the other course. If you are going to switch, do it soon!
  6. I would like to switch sections within 104, what should I do?
    • If you have a time conflict, there is no problem. If you want to switch to another section at the same time, be prepared for a possible refusal --- the instructor may not have room for another student. Course and section changes must be made through SCORE.
  7. 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.