# Math 101/102

### Calculus I with Precalculus Review

Two-semester treatment of (mostly) differential calculus. Includes an introduction to integration as well. Compared to MAT103, which covers the same calculus topics, the slower pace of MAT101/102 allows more in-class review of fundamental precalculus material including basic trigonometry, the graphs and properties of standard functions (e.g. logarithms, exponentials), inverse functions, algebraic techniques for solving equations (e.g. factoring, completing the square), equations for ellipses, hyperbolas and parabolas.

103 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.

101 typically covers somewhat more than the first half of 103. 102 begins with a review of differentiation and applications of the derivative and finishes up with definite integrals and the fundamental theorem of calculus.

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).

Notes:

• Although the Math Department considers this sequence to be equivalent to 103, students need to know that some Princeton programs will not accept 101/102 instead of 103.
• 101 is offered only in Fall, usually at 10MWF. 101 does not fulfill the QR requirement.
• 102 is offered only in Spring, usually at 11MWF and it does count as a QR.

### Who Takes this Sequence?

• Enrollment in this sequence is small (usually between 20 and 30 students) and most students who take only one semester of calculus will take 103 instead to finish up their math in a single semester.
• 101/102 is intended only for students whose precalculus background has significant gaps. Some have had a bit of calculus in high school, but some have not. It is a good choice for students for whom knowing a little calculus is useful but not a high priority. This includes students who plan to pursue a non-quantitative social science or humanities major.
• Many pre-med students choose to take this sequence. It appeals to students who don't need much calculus and are willing to invest two Princeton semesters so they can better balance math with a heavy time commitment to sports, other demanding courses, or important extra-curricular activities at which they excel.
• Students with math SAT scores above 700 should start in 103 even if they did not take calculus in high school.
• Students who should not take this course:
• Students who scored 3 or higher on the AB or BC calculus exam
• Prospective engineers or others who need to take the full 3-semester calculus sequence (103/104/201)

### Placement and Prerequisites

• This course has no formal prerequisites although we do assume that students have had some precalculus courses (trigonometry and algebra) in high school.
• If your math SAT score < 600 we strongly recommend 101/102 instead of 103.
• If you are not sure whether you belong in 103 or in 101, because, say, your math SAT is 690, but you never took calculus before, then sign up for 103 at the same time that 101 is offered to make it easier to switch should that become necessary later in the semester.

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!

101 Midterm Exam Solutions, 102 Midterm Review Solutions 102 Sample Final Exam Solutions.

It may also be useful to look at the sample exams posted for 103.

### FAQ

1. How hard should I expect to work?
• These courses require 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. What if I decide later that I need more calculus? Will this sequence get me ready for MAT104?
• If you did well (at least B+) in 101/102 and you are motivated enough to work hard, then you should know enough to take 104. You may need extra practice working through problems in order to do well in 104 just because the other students there may be more highly motivated and/or mathematically seasoned than your classmates in 101/102 were. With work it is certainly feasible.
3. How hard is it to get an A in this class? I absolutely have to get an A so I can go to medical school!
• Sigh. There are no guarantees, and we hope that you will still be able to go to med school, even if you sometimes get a B in a difficult math or science course. 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, in the larger courses like MAT103, the top 25% of 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. In smaller classes like 101/102 we don't follow this curve as strictly, but we use it as a guide. Our aim is that students will only get an A in MAT102 if they have learned the first semester of calculus well.
4. 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.