# uOttawa MAT 1322 Calculus II: Syllabus, Topics and Practice

> A study guide for University of Ottawa MAT 1322 (Calculus II): improper integrals, differential equations, series, Taylor series and partial derivatives.

Source: https://practicecalculus.com/courses/university-of-ottawa-mat-1322
Updated: 2026-11-08

## At a glance

- **Course code:** MAT 1322
- **Units:** 3 (lecture and discussion group)
- **Prerequisites:** MAT 1320 or MAT 1321
- **Credit restriction:** MAT 1322, MAT 1303, MAT 1332 and MAT 1325 cannot be combined for units
- **Covers:** Improper integrals, applications of the integral, separable differential equations, Euler's method, sequences, series, Taylor's formula and series, functions of two and three variables, partial derivatives, chain rule, directional derivatives, tangent planes and normal lines
- **Next course:** MAT 2322 (Calculus III for Engineers)
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MAT 1322 is the 3-unit Calculus II course at the University of Ottawa, taught in English, after MAT 1320 or MAT 1321.
- It covers improper integrals, applications of the integral, separable differential equations and Euler's method.
- It covers sequences, series, Taylor's formula and Taylor series.
- It ends with functions of several variables, partial derivatives, directional derivatives and tangent planes.

**MAT 1322** is Calculus II at the University of Ottawa, the English-language course that follows MAT 1320 or MAT 1321. Since uOttawa already teaches integration techniques in Calculus I, MAT 1322 can spend its time on what you do with integrals, on differential equations and series, and on a first look at functions of several variables. This guide maps every MAT 1322 topic to free practice.

## What uOttawa MAT 1322 covers

The uOttawa catalogue lists: improper integrals; applications of the integral; separable differential equations; Euler's method for differential equations; sequences and series; Taylor's formula and series; functions of two and three variables; and partial derivatives, the chain rule, directional derivatives, tangent planes and normal lines. The course has lectures and discussion groups, and the prerequisite is MAT 1320 or MAT 1321.

That combines most of a standard **Calculus 2** with the first part of **Calculus 3**. Parametric and polar curves are not in the catalogue description.

## MAT 1322 topic map

| MAT 1322 topic | Practice | Read |
| --- | --- | --- |
| Improper integrals | [Infinite limits of integration](/learn/calculus-2/improper-integrals-and-applications/infinite-limits-of-integration), [infinite discontinuities](/learn/calculus-2/improper-integrals-and-applications/infinite-discontinuities) | [Improper integrals guide](/blog/improper-integrals) |
| Applications of the integral | [Volumes with washers](/learn/calculus-1/applications-of-integrals/volumes-washers), [arc length](/learn/calculus-2/improper-integrals-and-applications/arc-length-and-surface-area), [work](/learn/calculus-2/improper-integrals-and-applications/work) | [Volumes of revolution](/blog/volumes-of-revolution) |
| Separable 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) |
| Euler's method | [Euler's method](/learn/calculus-2/improper-integrals-and-applications/eulers-method) | [Slope fields](/learn/calculus-2/improper-integrals-and-applications/slope-fields) |
| Sequences | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Squeeze theorem](/theorems/squeeze-theorem) |
| Series and convergence | [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) |
| Taylor's formula | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials), [estimating with Taylor](/learn/calculus-2/power-series-parametric-polar/estimating-with-taylor) | [Taylor's theorem](/theorems/taylors-theorem) |
| Taylor series | [Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series guide](/blog/taylor-series) |
| Functions of two and three variables | [Functions of several variables](/learn/calculus-3/partial-derivatives/functions-of-several-variables) | |
| Partial derivatives and the chain rule | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives), [multivariable chain rule](/learn/calculus-3/partial-derivatives/multivariable-chain-rule) | [Partial derivatives guide](/blog/partial-derivatives) |
| Directional derivatives | [Gradient and directional derivatives](/learn/calculus-3/partial-derivatives/gradient-and-directional-derivatives) | [Gradient guide](/blog/gradient-and-directional-derivatives) |
| Tangent planes and normal lines | [Tangent planes](/learn/calculus-3/partial-derivatives/tangent-planes) | |

## MAT 1322 in the uOttawa sequence

| Course | Title | Main focus |
| --- | --- | --- |
| [MAT 1320](/courses/university-of-ottawa-mat-1320) | Calculus I | Derivatives, integration techniques, numerical integration |
| MAT 1322 | Calculus II | Improper integrals, ODEs, series, partial derivatives |
| [MAT 2322](/courses/university-of-ottawa-mat-2322) | Calculus III for Engineers | Multiple integrals and vector calculus |

MAT 1322 cannot be combined for units with MAT 1303, MAT 1332 or MAT 1325.

## Example problems at the MAT 1322 level

**1. An improper integral with a discontinuity.**

$$\int_0^1 \frac{dx}{\sqrt{x}} = \lim_{a\to 0^+}\big[2\sqrt{x}\big]_a^1 = 2$$

**2. Euler's method.** For $y' = y$, $y(0) = 1$ and step $h = 0.5$: $y_1 = 1 + 0.5(1) = 1.5$ and $y_2 = 1.5 + 0.5(1.5) = 2.25$, an estimate of $e \approx 2.718$.

**3. Taylor's formula.** The degree 3 Taylor polynomial of $\ln(1 + x)$ at $0$ is $x - \frac{x^2}{2} + \frac{x^3}{3}$.

**4. A normal line.** For the surface $x^2 + y^2 + z^2 = 14$ at $(1, 2, 3)$, the gradient $\langle 2, 4, 6 \rangle$ gives the normal line $\langle 1 + 2t,\; 2 + 4t,\; 3 + 6t \rangle$.

## How to do well in MAT 1322

- **Keep MAT 1320 techniques ready.** Improper integrals and applications assume fluent substitution, parts and partial fractions.
- **Write limits explicitly.** Every improper integral is a limit. Show it in your working.
- **Practise series reasoning.** Name the test, check its conditions, and state convergence or divergence clearly.
- **Change gears for several variables.** The last unit is new territory. Slow down and practise partial derivatives until holding variables constant feels natural.

> **Tip:** the gradient of $F(x, y, z)$ is normal to the level surface $F = c$. That gives both tangent planes and normal lines in one step.

## Frequently asked questions

### What is MAT 1322 at uOttawa?

MAT 1322 is Calculus II. The uOttawa catalogue lists improper integrals; applications of the integral; separable differential equations; Euler's method; sequences and series; Taylor's formula and series; functions of two and three variables; and partial derivatives, the chain rule, directional derivatives, tangent planes and normal lines.

### What do I need for MAT 1322?

MAT 1320 or MAT 1321.

### Does MAT 1322 cover integration by parts?

At uOttawa, integration by parts, substitution and partial fractions are already listed in MAT 1320, so MAT 1322 uses them rather than teaching them from scratch.

### What comes after MAT 1322?

Engineering students take MAT 2322, Calculus III for Engineers, which also needs MAT 1341 or CEGEP linear algebra. Other programs list their own next course, so check your program requirements.