Yale MATH 1150 Integral Calculus and Series: Topics and Practice

Yale MATH 1150 is the integral calculus course in Yale's introductory sequence, the course long known as MATH 115. The math department's guide says it investigates the mathematics of accumulation: using information about instantaneous rates, such as velocity, to compute net change, such as change in position. This guide maps every MATH 1150 topic to free practice with instant feedback.

What MATH 1150 covers

According to the Yale math department's introductory course guide, MATH 1150 has three strands. The first is integral calculus itself, turning rates into net changes. The second is series: convergence tests and Taylor series, which the guide says help explain how calculators work. The third is a set of applications that take single-variable calculus further, including solids of revolution, parametric equations and polar coordinates.

Throughout the semester, the guide says, students consider both exact and approximate solutions and investigate the role of error. That makes MATH 1150 a close match for a standard Calculus 2 course.

MATH 1150 topic map

Placement and MATH 1160

MATH 1150 requires the placement exam, unless you completed MATH 1110 or MATH 1120 at Yale. The department says students typically place into MATH 1150 after a differential calculus course such as AP Calculus AB.

MATH 1160 is the sister course. It covers integral calculus with an emphasis on applications to biology, and the department recommends it for biology and pre-medical students. Either course can be used as the prerequisite for anything that requires MATH 1150.

Example problems at the MATH 1150 level

1. Net change from a rate. If velocity is v(t) = 3t^2 meters per second, the change in position from t = 0 to t = 2 is

2. A geometric series.

3. A Taylor polynomial. The Maclaurin series of \sin x starts x - \frac{x^3}{6} + \frac{x^5}{120}, so \sin(0.2) \approx 0.2 - 0.00133 = 0.19867, with an error smaller than the next term.

How to do well in MATH 1150

• Think in terms of accumulation. Every integral question gets easier if you ask what is being added up. Practice with accumulation functions.
• Learn when to use each series test. The choosing a test lesson trains exactly that decision.
• Track your error. The course cares about approximations, so always ask how big the error could be, using the alternating series test or Taylor's remainder.
• Practice mixed sets before exams. The series practice mixes problem types the way exams do.

Next comes multivariable calculus: see the MATH 1200 guide.