# McMaster MATH 1AA3 Calculus for Science II: Topics and Practice > A study guide for McMaster MATH 1AA3: integration techniques, differential equations, polar and parametric curves, series and partial derivatives. Source: https://practicecalculus.com/courses/mcmaster-math-1aa3 Updated: 2026-11-08 ## At a glance - **Course code:** MATH 1AA3 - **Units:** 3 (three lectures and one tutorial, one term) - **Prerequisites:** One of MATH 1A03, 1LS3, 1X03 or 1ZA3; or at least B- in MATH 1M03 - **Antirequisites:** ARTSSCI 1D06 A/B, MATH 1LT3, 1XX3, 1ZB3 - **Restrictions:** Not open to students in Mathematics and Statistics I, or with credit or registration in ISCI 1A24 A/B - **Covers:** Techniques of integration, applications of definite integrals, differential equations, polar coordinates, parametrized curves, sequences, infinite series, power series, partial derivatives, double integrals - **Practice here:** [Calculus 2](/learn/calculus-2) ## Key takeaways - MATH 1AA3 is McMaster's 3-unit Calculus for Science II, taken after MATH 1A03 or an equivalent. - It covers more integration techniques, applications of definite integrals and differential equations. - It adds polar coordinates, parametrized curves, sequences, infinite series and power series. - It ends with a short introduction to partial derivatives and double integrals. **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 topic | Practice | Read | | --- | --- | --- | | Integration by parts | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts) | [Integration by parts guide](/blog/integration-by-parts) | | Trig integrals and substitution | [Trig integrals](/learn/calculus-2/integration-techniques/trig-integrals), [trig substitution](/learn/calculus-2/integration-techniques/trig-substitution) | [Trig substitution guide](/blog/trig-substitution) | | Partial fractions | [Partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Partial fractions guide](/blog/partial-fractions) | | Applications of definite integrals | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves), [volumes](/learn/calculus-1/applications-of-integrals/volumes-washers), [arc length](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area) | [Volumes of revolution](/blog/volumes-of-revolution) | | Differential equations | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations), [logistic growth](/learn/calculus-2/improper-integrals-and-applications/logistic-growth) | [Slope fields](/learn/calculus-2/improper-integrals-and-applications/slope-fields) | | Polar coordinates | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates), [polar area](/learn/calculus-2/power-series-parametric-polar/polar-area) | | | Parametrized curves | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | [Parametric arc length](/learn/calculus-2/power-series-parametric-polar/parametric-arc-length) | | Sequences | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Squeeze theorem](/theorems/squeeze-theorem) | | Infinite series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums), [choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests), [geometric series](/blog/geometric-series) | | Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius), [Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Power series guide](/blog/power-series) | | Partial derivatives | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Partial derivatives guide](/blog/partial-derivatives) | | Double integrals | [Iterated integrals](/learn/calculus-3/multiple-integrals/iterated-integrals) | [Double integrals guide](/blog/double-integrals) | ## MATH 1AA3 in the McMaster sequence | Course | Title | Main focus | | --- | --- | --- | | [MATH 1A03](/courses/mcmaster-math-1a03) | Calculus for Science I | Limits, derivatives, first integrals | | MATH 1AA3 | Calculus for Science II | Integration, ODEs, curves, series, intro to several variables | 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.** $$\int \frac{3x + 1}{(x - 1)(x + 1)}\,dx = 2\ln|x - 1| + \ln|x + 1| + C$$ **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](/learn/calculus-2/integration-techniques/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. ## Frequently asked questions ### What is MATH 1AA3 at McMaster? MATH 1AA3 is Calculus for Science II. The McMaster calendar lists additional techniques of integration, applications of definite integrals, differential equations, polar coordinates and parametrized curves, then sequences, infinite series and power series, and finally partial derivatives and double integrals. ### What do I need for MATH 1AA3? One of MATH 1A03, 1LS3, 1X03 or 1ZA3, or a grade of at least B- in MATH 1M03. ### Is MATH 1AA3 hard? It covers many topics in one term, from integration to series to double integrals. Series in particular are new for most students. Steady weekly practice and the tutorials make a big difference. ### Can engineering students take MATH 1AA3? MATH 1ZB3 is an antirequisite, so engineering students normally take the engineering mathematics sequence instead. MATH 1AA3 is for science students.