McMaster MATH 1AA3 Calculus for Science II: Topics and Practice

MATH 1AA3 is Calculus for Science II at McMaster University, the second calculus course for science students after MATH 1A03. It is a busy one-term course: more integration, differential equations, new ways to describe curves, a full unit on series, and a short first look at calculus in several variables. This guide maps every MATH 1AA3 topic to free practice so you can keep up with the pace.

What McMaster MATH 1AA3 covers

The McMaster undergraduate calendar lists the topics as additional techniques of integration, applications of definite integrals, differential equations, polar coordinates and parametrized curves; sequences, infinite series and power series; and partial derivatives and double integrals. The format is three lectures and one tutorial a week for one term, worth 3 units. You need one of MATH 1A03, 1LS3, 1X03 or 1ZA3, or at least B- in MATH 1M03.

The link above points to the 2025-2026 calendar entry, the most recent individual course page we could confirm. Check the current McMaster calendar for any changes.

That is a complete Calculus 2 course with a preview of Calculus 3 at the end.

MATH 1AA3 topic map

MATH 1AA3 in the McMaster sequence

Its antirequisites include MATH 1LT3, 1XX3 and 1ZB3, so you count only one of these second courses.

Example problems at the MATH 1AA3 level

1. Partial fractions.

2. A logistic model. In \frac{dP}{dt} = 0.2P\left(1 - \frac{P}{500}\right), the population grows fastest when P = 250, half the carrying capacity.

3. A parametric slope. For x = t^2, y = t^3: \frac{dy}{dx} = \frac{3t^2}{2t} = \frac{3t}{2}.

4. A power series. \frac{1}{1 + x^2} = \sum (-1)^n x^{2n} for |x| < 1, and integrating gives \arctan x = x - \frac{x^3}{3} + \frac{x^5}{5} - \cdots.

How to do well in MATH 1AA3

• Pace yourself across topics. There are many short units. Keep up each week rather than catching up before tests.
• Practise choosing integration methods. Mixed sets such as choosing a strategy build the decision skill.
• Learn the main series. Geometric series and the Maclaurin series for e^x, \sin x and \cos x unlock most power series problems.
• Use tutorials. The weekly tutorial is the best time to work through series and polar problems with help.

Tip: for a power series, find the radius with the ratio test, then test each endpoint separately. Endpoints often behave differently.