Course MAT104 in Fall 2011

Calculus II (One Variable, Continued from 103)

Second semester of the 3-semester calculus sequence 103/104/201.  Main topics are Integration and Series.  Offered Fall and Spring.


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.

Description of Classes

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.

  • Roughly equivalent to BC calculus or to the mandatory and optional calculus portion of Math HL in the IB program.
  • It is impossible to do well in 201 without a solid knowledge of the material in this course.
  • Students who plan to do math-track economics or finance should take this course, followed by 201.  Prospective economics majors who are not math-track can take 175 instead.
Who Takes This Course

This is the usually the right course for students who took AB calculus in high school and got a 5 on the AP exam.

  • Students with a strong interest in math as major who received a 5 on the AB calculus exam and have a SAT math score > 760 can consider an introductory proof-based course like 215 or perhaps 214. Consultation with the math placement officer is strongly advised.
  • Students who got a 4 on the AB exam should take 103 instead.   Even students who took BC calculus in high school find that they need to work hard in this course.   See Placement and Prerequisites below.

Most of the students in this course plan to major in science or engineering or economics. Math majors rarely take this course, but it does happen. About half the students in 104 will continue on to 201 the following semester. 

In the fall semester, most of the students are incoming freshmen with AP credit for first semester calculus 103. In the spring semester about half the students are continuing from 103 in the fall.

This is the best choice for students who used to know calculus but their skills are rusty from disuse after a gap in their mathematical studies. Because it makes heavy use of the prerequisite material from precalculus courses and also from 103, it gives a thorough review of all of high school mathematics in a single semester. This may also explain why many students consider it to be significantly harder than 103.

Placement and Prerequisites:
  • A basic knowledge of differential calculus and integration from Calculus I is assumed. See 103 for details on how to tell if you are qualified to skip the first semester of calculus and start in 104.
  • We estimate that any of the following:
    • a 5 on the BC calculus exam
    • a 7 on the IB MathHL exam
    • an A on the British A-levels exam

    is minimally equivalent to 104, comparable to a grade of C.

  • Be warned that the pace is extremely fast and the mastery of calculus expected by the end of 104 is typically much higher than in high school or in the BC calculus curriculum. If your math SAT score is below 650 and/or your differential calculus is weak or rusty, you may want to start in 103 instead.
  • If your math SAT score < 600 you should seriously consider starting in 103 instead of 104.
  • If you are not sure whether you belong in 103 or in 104, then sign up for 104 and be prepared to switch in drop/add.

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

Sample Material

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 SolutionsFinal 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. 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.
  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?
  6. I would like to switch sections within 104, what should I do?
    • If you have a time conflict, there is no problem.  We will find a spot for you. 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.  More information can be found in Forms & Procedures.
  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.