Dalhousie MATH 1010 Calculus II: Syllabus, Topics and Practice

MATH 1010 is Differential and Integral Calculus II at Dalhousie University, the continuation of MATH 1000. It is the classic second calculus course: more integration, a first look at differential equations, new ways to describe curves, and infinite series. This guide maps each MATH 1010 topic to free practice so you can build every skill with short problems and instant feedback.

What Dalhousie MATH 1010 covers

The Dalhousie calendar lists the topics as Riemann sums, techniques of integration, elementary differential equations and applications, parametric equations and polar coordinates, sequences and series, and Taylor series. The course has lectures and tutorials, and the prerequisite is MATH 1000, MATH 1215 or MATH 1280.

This is a standard Calculus 2 course. Riemann sums appear at the start because MATH 1000 introduces definite integrals mainly through antiderivatives, and MATH 1010 grounds them properly before moving on.

MATH 1010 topic map

MATH 1010 in the Dalhousie sequence

Example problems at the MATH 1010 level

1. Integration by parts twice. For \int x^2 e^x\,dx, apply parts with u = x^2, then again with u = x:

2. Area in polar coordinates. The area inside r = 2\sin\theta is

3. A geometric series. \sum_{n=0}^{\infty} \left(\tfrac{2}{3}\right)^n = \frac{1}{1 - 2/3} = 3.

4. A Taylor series. \sin x = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \cdots, so \lim_{x\to 0}\frac{\sin x - x}{x^3} = -\frac{1}{6}.

How to do well in MATH 1010

• Use your tutorials. MATH 1010 has a tutorial component in the calendar. Bring the problems that stumped you.
• Build a technique checklist. Substitution first, then parts, trig methods and partial fractions. Mixed practice is the key skill.
• Learn the standard series. Geometric series, p-series and the main Maclaurin series are the reference points for every comparison.
• Graph polar curves before integrating. A sketch shows the right limits for \theta and stops you from counting a loop twice.

A weekly study plan for MATH 1010

1. Early in the week: watch or reread the lecture, then do the matching lesson here, such as integration by parts or series and partial sums.
2. Midweek: work the assigned problems without notes first. Mark every problem you could not start.
3. Before the tutorial: bring the marked problems and ask about the first step, not the full solution.
4. End of the week: do a short mixed review that includes older topics, so integration skills stay fresh when you reach series.

Spacing practice like this is far more effective than long sessions right before a midterm. Our guide on how to study calculus explains why.

Tip: if the ratio test gives a limit of exactly 1, it tells you nothing. Switch to a comparison or the integral test.