# Dalhousie MATH 1010 Calculus II: Syllabus, Topics and Practice

> A study guide for Dalhousie MATH 1010 (Differential and Integral Calculus II): integration techniques, ODEs, polar curves and Taylor series.

Source: https://practicecalculus.com/courses/dalhousie-math-1010
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 1010.03
- **Credit hours:** 3 (lecture and tutorial)
- **Prerequisites:** MATH 1000.03, MATH 1215.03 or MATH 1280.03
- **Equivalent:** MATH 1290.03
- **Covers:** Riemann sums, techniques of integration, elementary differential equations, parametric equations and polar coordinates, sequences and series, Taylor series
- **Next course:** MATH 2001 (Intermediate Calculus I)
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 1010 is the 3 credit hour Calculus II course at Dalhousie, with lectures and tutorials.
- It covers Riemann sums and the main integration techniques.
- It adds elementary differential equations, parametric equations and polar coordinates.
- It ends with sequences, series and Taylor series, and leads to MATH 2001.

**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 topic | Practice | Read |
| --- | --- | --- |
| Riemann sums | [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums guide](/blog/riemann-sums) |
| 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) |
| Choosing a technique | [Choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) | [Common calculus mistakes](/blog/common-calculus-mistakes) |
| Elementary differential equations | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Growth and decay](/learn/calculus-2/improper-integrals-and-applications/growth-and-decay) |
| Parametric equations | [Parametric curves](/learn/calculus-2/power-series-parametric-polar/parametric-curves) | [Parametric arc length](/learn/calculus-2/power-series-parametric-polar/parametric-arc-length) |
| Polar coordinates | [Polar coordinates](/learn/calculus-2/power-series-parametric-polar/polar-coordinates) | [Polar area](/learn/calculus-2/power-series-parametric-polar/polar-area) |
| Sequences | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Squeeze theorem](/theorems/squeeze-theorem) |
| Series and convergence | [Choosing a test](/learn/calculus-2/sequences-and-series/choosing-a-test) | [Convergence tests](/blog/convergence-tests), [geometric series](/blog/geometric-series) |
| Taylor series | [Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series guide](/blog/taylor-series) |

## MATH 1010 in the Dalhousie sequence

| Course | Title | Main focus |
| --- | --- | --- |
| [MATH 1000](/courses/dalhousie-math-1000) | Differential and Integral Calculus I | Limits, derivatives, first integrals |
| MATH 1010 | Differential and Integral Calculus II | Integration, ODEs, polar, series |
| [MATH 2001](/courses/dalhousie-math-2001) | Intermediate Calculus I | Vectors and several variables |

## 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 $u = x$:

$$\int x^2 e^x\,dx = e^x(x^2 - 2x + 2) + C$$

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

$$\frac{1}{2}\int_0^{\pi} 4\sin^2\theta\,d\theta = \pi$$

**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](/learn/calculus-2/integration-techniques/integration-by-parts) or [series and partial sums](/learn/calculus-2/sequences-and-series/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](/blog/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.

## Frequently asked questions

### What is MATH 1010 at Dalhousie?

MATH 1010 is Differential and Integral Calculus II. The calendar describes it as a continuation of calculus with Riemann sums, techniques of integration, elementary differential equations and applications, parametric equations and polar coordinates, sequences and series, and Taylor series.

### What do I need for MATH 1010?

MATH 1000, MATH 1215 or MATH 1280. MATH 1010 is equivalent to MATH 1290, so you can only count one of them.

### Is MATH 1010 harder than MATH 1000?

Most students find it harder. Integration techniques need a lot of practice, and series ask you to reason about convergence rather than just compute. Steady weekly work and the tutorials help a lot.

### What comes after MATH 1010?

MATH 2001, Intermediate Calculus I, which needs MATH 1010 and covers vectors, vector functions, partial derivatives and multiple integrals.