Yale MATH 1120 Differential Calculus: Topics and Practice

Yale MATH 1120 is the differential calculus course in Yale's introductory sequence, the course long known as MATH 112. The math department's guide says its goal is to measure a function's instantaneous rate of change, the derivative, and to use that idea to understand how functions behave. This guide lists what MATH 1120 covers and links each topic to free practice with instant feedback.

What MATH 1120 covers

The Yale math department's introductory course guide describes MATH 1120 in four steps. First, the course defines limits, which make it possible to talk rigorously about instantaneous change. Next, it defines the derivative and develops rules that simplify computing it. Then it applies the derivative to understand function behavior, with examples such as minimizing cost or maximizing profit in economic models. Finally, it develops strategies for reversing differentiation to find antiderivatives, which have applications such as computing areas and modeling population growth.

That makes MATH 1120 a close match for a standard Calculus 1 course. It stops before the full treatment of integration, which belongs to MATH 1150.

MATH 1120 topic map

Placement and the MATH 1100/1110 option

MATH 1120 requires Yale's calculus placement exam, and the department says students typically take it after finishing pre-calculus. If your pre-calculus is shaky, the department offers MATH 1100 and 1110, a two-semester sequence that integrates pre-calculus and differential calculus. Completing both counts the same as MATH 1120 for majors and professional school requirements such as pre-med, and earns two course credits instead of one course.

If you already have strong differential calculus, for example from AP Calculus AB, the placement exam may place you directly into MATH 1150.

Example problems at the MATH 1120 level

1. A derivative from the rules. For f(x) = x^3 - 6x^2 + 9x, f'(x) = 3x^2 - 12x + 9 = 3(x - 1)(x - 3).

2. Function behavior. From that factorization, f increases on (-\infty, 1), decreases on (1, 3) and increases again on (3, \infty), so it has a local maximum at x = 1 and a local minimum at x = 3.

3. An antiderivative.

How to do well in MATH 1120

• Make the limit idea concrete. Work through average and instantaneous rate of change until the derivative feels like a speedometer reading.
• Drill the derivative rules daily. Short sessions with the derivative rules practice build speed for exams.
• Connect graphs and derivatives. Many questions ask what a derivative tells you about a graph, so practice reading both directions.
• Keep formulas close. The formula sheet puts every basic derivative on one page.

When you are ready for integration, read the MATH 1150 guide.