NYU MATH-UA 121 Calculus I: Topics, Study Guide and Practice

NYU MATH-UA 121 is Calculus I in NYU's College of Arts and Science, the starting point for students heading into math, science, economics and pre-health tracks that require calculus. It is a full one-semester introduction to single-variable calculus. This guide lines up each MATH-UA 121 topic with a lesson you can practice right away, with instant feedback on every answer.

What NYU MATH-UA 121 covers

The NYU bulletin describes MATH-UA 121 as a course on derivatives, antiderivatives and integrals of functions of one variable. Applications include graphing and optimization, and the course builds to the definite integral, the Fundamental Theorem of Calculus, and using integrals to find areas and volumes.

That is a textbook Calculus 1: limits and continuity first, then derivatives and their rules, then applications, then integration. It matches the full Calculus 1 path on PracticeCalculus almost unit for unit.

MATH-UA 121 topic map

Where MATH-UA 121 sits in the NYU sequence

NYU also runs a separate Mathematics for Economics sequence (MATH-UA 131, 132, 133). The bulletin notes that students cannot take both that sequence and the standard Calculus I to III sequence, so check which one your major requires before you register.

Example problems at the MATH-UA 121 level

1. A zero over zero limit. Evaluate \lim_{x \to 3} \frac{x^2 - 9}{x - 3}.

Factor and cancel: \frac{(x-3)(x+3)}{x-3} = x + 3, so the limit is 3 + 3 = 6.

2. A product rule derivative. Differentiate f(x) = x^3 e^x.

3. A definite integral with the Fundamental Theorem.

How to do well in MATH-UA 121

• Start with the warm-up. If MATH-UA 9 was a while ago, the functions warm-up rebuilds exponent, log and trig skills before limits begin.
• Make the derivative rules automatic. Most of the semester leans on the product rule, quotient rule and chain rule. Drill them until you do not have to think.
• Watch for the classic slips. Our list of common calculus mistakes covers dropped chain rule factors, sign errors and forgotten constants.
• Keep the formula sheet nearby while you practice. The calculus formula sheet has every rule on one page.
• Rehearse before each exam with timed practice exams, and follow our guide on how to prepare for a calculus exam.

Tip: optimization problems are the most common place students lose points. Write the quantity you are maximizing as a function of one variable first, then differentiate.