MAT104 Calculus II

Schedule: MWF at 9AM, at 10AM, at 11AM or at 12:30PM, Fall and Spring. Optional review sessions are very helpful, but they are scheduled only after classes begin.

Brief Course Description: Second semester of the standard 3-semester calculus sequence. Topics include techniques and applications of integration including area, length and volume and an introduction to differential equations. Introduces complex numbers and polar coordinates, analysis of convergence of infinite series and improper integrals, approximation using Taylor’s theorem with remainder. Emphasizes the development of mature problem-solving skills through problems that require sophisticated pattern-recognition and the ability to apply and adapt multiple techniques to solve a single problem.

Why take this course? The topics in this course are of fundamental importance in the natural sciences, engineering and finance.  

Prerequisites:  MAT103 or equivalent. More than that, this course requires expert familiarity (without a calculator) in working with the standard library of functions: polynomials, rational and root functions, logarithms and exponentials, trigonometric functions and their inverses. This includes solving equations with these functions, computing their derivatives and sketching their graphs. Problems tend to involve multiple techniques and fluency in all the standard algebraic manipulations.

Who takes this course? Most students in this course are first-year students planning to major in one of the natural sciences, engineering, math-track economics or finance. Some math majors start with this course and then take 215 in the spring.

Placement Information:  MAT104 is roughly equivalent to BC calculus or the mandatory calculus portion of Math HL in the IB program. We estimate that any one of the following is minimally equivalent to this course, comparable to a grade of C: 5 on the BC exam or 7 on the IB Math HL exam or an A on the British A-levels exam. Two years of high school calculus with good grades may be comparable, but it is difficult to say for sure, since programs can vary quite a bit.

If you are undecided, go with the more ambitious choice, but be prepared to adjust during the drop/add period. There will be a placement quiz early in the semester to help you confirm whether you have chosen the right math course. Please take the results of the placement quiz seriously. Although jumping ahead of your recommended placement is not always impossible, remember that the pace and the work-load in a university course will not be like high school. Your work load will be quite demanding even if you are in the right course. Learning two math courses in a single semester will be excessively stressful and should not be undertaken lightly.

Talk to your advisers and listen to what they say at least as seriously as you listen to your friends.  Advice from other students does not always take into account the differences in background and learning styles that may be relevant to your decisions.


  • Your math placement says 104/175. What does that even mean? If you need to take 201-202 for your program (required for B.S.E), then you will need 104. If you want to do finance or math-track economics, then 104 is the right choice. 175 is a less intensive version of multivariable calculus. Along with 103 it minimally satisfies the prerequisites for the economics major but it is not at all optimal for finance.  The 175 web page will have more detailed information.
  • You want to take 104 but it is probably a stretch based on your test scores. Your advisers are telling you to take 103 instead but that does not feel right to you. If you really believe that you belong in 104, you can try it. Switching classes is easy during drop/add. But be honest with yourself as you get more information from the placement quiz and throughout the drop/add period. MAT104 is significantly harder than 103, and you will pay a high price in stress and in GPA if you are not adequately prepared. Try the sample problems from 103. If you can solve most of those problems, go ahead and sign up for MAT104 but take the placement quiz results seriously. Seek help early!
  • You don't have any standardized test scores but you took calculus in high school. Try the sample problems for the calculus courses you consider. If the problems look mostly familiar and you can actually solve at least half of them, then it makes sense to try the next course up in the sequence and drop back if necessary during the drop/add period.
  • You want to be an engineer and you are worried that you will be behind unless you start in 201. Your best path to completing the BSE program is to start in the course that is the best fit for your current knowledge. You can take courses over the summer to complete missing prerequisites. Taking courses that you can successfully complete is the most efficient plan in the long run. Many successful BSE students start in 103 or 104.
  • You want to be an engineer and EGR192 sounds really exciting. You really want to talk your way into that class but if you need 104 that's a deal-breaker. Please read the previous answer. Getting a C or worse is a real possibility if you don’t have enough background. For an integrated course your options are severely limited once drop/add ends. Dropping math means also dropping physics because the integrated courses have less flexibility.
  • What kind of calculator do you need for calculus at Princeton? The math department courses do not use calculators. If you normally rely on your calculator to translate a function or equation into a graph, to solve equations, or to find values of trigonometric functions at the standard angles, then 104 will be very challenging. Consider 103 instead.
  • Are you serious about no calculators? Why? Calculators can be useful, but these courses want to teach students how to think independently in a quantitative setting and calculators can function as substitute for thinking at the beginning. Students need to learn the basic vocabulary and grammar of mathematics so that they can recognize patterns and common features by working through simple well-chosen examples. For instance, a program like 'Google translate' can be helpful to a person with basic knowledge of a language to decipher a complicated sentence or even to write a correct one, but without a good foundation to refine and direct its application, the results of blindly applying this useful technological tool can be wildly off the mark.
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