# Course MAT103

## Calculus I

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. Usually offered MWF at 10 and 11 in the spring semester.

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.

*Rougly* equivalent to AB calculus or to the mandatory calculus portion of Math HL in the IB program.

A frequent choice to fulfill the QR requirement.

Most of the students in this course are incoming freshmen, many of whom are still undecided about a major. If you consider economics or any of the sciences, then a strong working knowledge of the topics of this course is a must. Many pre-med students take this course. Math and physics majors typically start in 215 or 203 or 216. The majority of engineering majors start calculus in 104 or higher.

We estimate that any one of the following:

- a 4 on the AB calculus exam (or the AB subscore of the BC exam)
- a 6 on the IB MathHL exam
- a B on the British A-levels exam
- a year of calculus with good grades (B+ or higher) at better high schools

is *minimally* equivalent to this course, comparable to a grade of C in MAT103.

The only prerequisite for this course is a solid precalculus background from high school. A math SAT score of 700 or more is a good indication that you are ready for this course, even if you did not have calculus in high school, as no prior knowledge of calculus is assumed. Be warned however that the pace is extremely fast and the mastery of calculus expected by the end of the course is typically much higher than in high school.

If your math SAT score < 600 we strongly recommend that you start in 100 to prepare for 103.

If you are not sure whether you belong in 103 or in 100, because, say, your math SAT is 690, but you never took calculus before, then sign up for 103 *at the same time that 100 is offered* to make it easier to switch should that become necessary later in the semester. In that case you will need to follow up by taking 103 in the spring semester.

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

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.

- 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.

- 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 typically curved. Historically, approximately 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. We do sometimes give D's or F's, but this is rare.

- 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.