# UCalgary MATH 267 University Calculus II: Topics and Practice

> A study guide for University of Calgary MATH 267: integration techniques, series, Taylor series, partial derivatives and multiple integrals.

Source: https://practicecalculus.com/courses/university-of-calgary-math-267
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 267
- **Units:** 3, hours (3-1)
- **Prerequisites:** 3 units from Mathematics 249, 265 or 275
- **Antirequisites:** Credit for MATH 267 and 277 will not be allowed
- **Covers:** Techniques of integration, sequences, series, convergence tests, Taylor series, partial differentiation, multiple integration, parametric equations and applications
- **Practice here:** [Calculus 2](/learn/calculus-2)

## Key takeaways

- MATH 267 is a 3-unit course that finishes single variable calculus and introduces calculus in several variables.
- The single variable part covers integration techniques, sequences, series, convergence tests and Taylor series.
- The several variable part covers partial differentiation, multiple integration and parametric equations.
- It follows MATH 249, 265 or 275, and cannot be combined for credit with MATH 277.

**MATH 267** is University Calculus II at the University of Calgary. The calendar calls it a concluding treatment of single variable calculus and an introduction to calculus in several variables, which means it packs parts of a usual Calculus 2 and Calculus 3 into one term. This guide maps each MATH 267 topic to free practice so you can keep up with the pace one short lesson at a time.

## What UCalgary MATH 267 covers

The University of Calgary calendar lists two blocks. Single variable calculus: techniques of integration, sequences, series, convergence tests and Taylor series. Calculus of several variables: partial differentiation, multiple integration, parametric equations and applications. The course is worth 3 units with 3 hours of lecture and 1 hour of tutorial per week, and needs 3 units from MATH 249, 265 or 275.

Compared with the usual split, MATH 267 is the core of **Calculus 2** (techniques and series) plus the start of **Calculus 3** (partial derivatives and multiple integrals). Because MATH 265 already covered improper integrals and applications of integration, MATH 267 can move quickly.

## MATH 267 topic map

| MATH 267 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) |
| Sequences | [Sequences](/learn/calculus-2/sequences-and-series/sequences) | [Squeeze theorem](/theorems/squeeze-theorem) |
| Series | [Series and partial sums](/learn/calculus-2/sequences-and-series/series-and-partial-sums) | [Geometric series](/blog/geometric-series), [geometric series formula](/rules/geometric-series-formula) |
| Convergence tests | [Comparison tests](/learn/calculus-2/sequences-and-series/comparison-tests), [ratio and root tests](/learn/calculus-2/sequences-and-series/ratio-and-root-tests) | [Convergence tests](/blog/convergence-tests) |
| Taylor series | [Taylor polynomials](/learn/calculus-2/power-series-parametric-polar/taylor-polynomials), [Maclaurin series](/learn/calculus-2/power-series-parametric-polar/maclaurin-series) | [Taylor series guide](/blog/taylor-series) |
| Partial differentiation | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives), [chain rule](/learn/calculus-3/partial-derivatives/multivariable-chain-rule) | [Partial derivatives guide](/blog/partial-derivatives) |
| Multiple integration | [Iterated integrals](/learn/calculus-3/multiple-integrals/iterated-integrals), [polar double integrals](/learn/calculus-3/multiple-integrals/polar-double-integrals) | [Double integrals guide](/blog/double-integrals) |
| 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) |
| Applications | [Double integral applications](/learn/calculus-3/multiple-integrals/double-integral-applications) | |

## MATH 267 in the UCalgary sequence

| Course | Title | Comes after |
| --- | --- | --- |
| [MATH 265](/courses/university-of-calgary-math-265) | University Calculus I | Math 30-1 and Math 31 |
| MATH 267 | University Calculus II | MATH 249, 265 or 275 |
| MATH 277 | Multivariable Calculus for Engineers and Scientists | MATH 275 and MATH 211 (credit with 267 not allowed) |

Engineering students usually go from [MATH 275](/courses/university-of-calgary-math-275) to MATH 277 instead of MATH 267.

## Example problems at the MATH 267 level

**1. Partial fractions.**

$$\int \frac{1}{x^2 - 1}\,dx = \frac{1}{2}\ln\left|\frac{x - 1}{x + 1}\right| + C$$

**2. A p-series.** $\sum \frac{1}{n^2}$ converges because $p = 2 > 1$, while the harmonic series $\sum \frac{1}{n}$ diverges.

**3. A Maclaurin series.** $\frac{1}{1 - x} = 1 + x + x^2 + \cdots$ for $|x| < 1$. Integrating gives $-\ln(1 - x) = x + \frac{x^2}{2} + \frac{x^3}{3} + \cdots$.

**4. A double integral.**

$$\int_0^2\int_0^1 (x + y)\,dy\,dx = \int_0^2 \left(x + \tfrac{1}{2}\right)dx = 3$$

## How to do well in MATH 267

- **Front-load integration practice.** The first weeks set the pace. Mixed sets like [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) make the technique choice automatic.
- **Learn which test fits which series.** Geometric and p-series for comparison, ratio test for factorials and powers, alternating series test for alternating signs.
- **Switch modes on purpose.** When the course turns to several variables, slow down and draw the regions.
- **Use tutorials for the hard step.** Bring the problems where you could not decide how to begin.

> **Tip:** to set up a double integral, decide the order first, then read the bounds off a sketch from the outside variable in.

## Frequently asked questions

### What is MATH 267 at the University of Calgary?

MATH 267 is University Calculus II. The UCalgary calendar calls it a concluding treatment of single variable calculus and an introduction to calculus in several variables: techniques of integration, sequences, series, convergence tests and Taylor series, then partial differentiation, multiple integration, parametric equations and applications.

### What do I need for MATH 267?

3 units from Mathematics 249, 265 or 275.

### MATH 267 vs MATH 277?

You cannot get credit for both. MATH 277, Multivariable Calculus for Engineers and Scientists, follows MATH 275 and MATH 211 and is fully multivariable, ending with optimization and Lagrange multipliers. MATH 267 still spends part of the term on single variable topics such as series.

### Is MATH 267 hard?

It covers a lot in one term: integration techniques, series and a first course in multivariable calculus. Students who practise integration early leave more time for series and multiple integrals later.