# UCalgary MATH 275 Calculus for Engineers: Topics and Practice

> A study guide for University of Calgary MATH 275 (Calculus for Engineers and Scientists): derivatives, integration, improper integrals and Taylor series.

Source: https://practicecalculus.com/courses/university-of-calgary-math-275
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 275
- **Units:** 3, hours (3-1T-1.5)
- **Prerequisites:** Mathematics 30-1 or Mathematics 2 (Continuing Education); and Mathematics 31 or Mathematics 3 (Continuing Education)
- **Antirequisites:** Credit for MATH 275 and either 249 or 265 will not be allowed
- **Covers:** Derivative laws, the Mean Value Theorem, optimization, curve sketching, the Fundamental Theorem, techniques of integration, improper integrals, areas of planar regions, power series, Taylor's theorem and Taylor series
- **Next course:** MATH 277 (Multivariable Calculus for Engineers and Scientists)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 275 is a 3-unit, applications-focused single variable calculus course for engineers and scientists at the University of Calgary.
- It covers differentiation, integration and infinite series in one term, so it reaches further than a typical Calculus 1.
- Its hours (3-1T-1.5) include a tutorial and an extra 1.5-hour component on top of lectures.
- It leads to MATH 277, which also needs MATH 211.

**MATH 275** is Calculus for Engineers and Scientists at the University of Calgary. The calendar calls it an extensive treatment of single variable calculus with an emphasis on applications, and it covers a lot: derivatives and their applications, the full integration toolkit, and power and Taylor series, all in one term. This guide maps every MATH 275 topic to free practice so you can keep up with its pace.

## What UCalgary MATH 275 covers

The University of Calgary calendar groups the topics in three parts. Differentiation: derivative laws, the Mean Value Theorem, optimization, curve sketching and other applications. Integral calculus: the Fundamental Theorem of Calculus, techniques of integration, improper integrals and areas of planar regions. Infinite series: power series, Taylor's theorem and Taylor series. The course is 3 units, with hours listed as (3-1T-1.5): three lecture hours, a one-hour tutorial and a further 1.5-hour component each week.

In standard terms, MATH 275 covers most of **Calculus 1** and the core of **Calculus 2** in a single course. Sequences and general convergence tests are not named in the description; the series part focuses on power series and Taylor series.

## MATH 275 topic map

| MATH 275 topic | Practice | Read |
| --- | --- | --- |
| Derivative laws | [Mixed rules practice](/learn/calculus-1/derivative-rules/derivative-rules-practice) | [Power rule](/rules/power-rule), [chain rule](/rules/chain-rule), [product rule](/rules/product-rule) |
| Inverse trig derivatives | [Inverse trig derivatives](/learn/calculus-1/derivative-rules/inverse-trig-derivatives) | [Derivative of arctan x](/derivatives/arctan-x) |
| The Mean Value Theorem | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Mean Value Theorem](/theorems/mean-value-theorem), [MVT guide](/blog/mean-value-theorem) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Curve sketching | [Increasing and decreasing](/learn/calculus-1/applications-of-derivatives/increasing-and-decreasing), [second derivative](/learn/calculus-1/applications-of-derivatives/second-derivative) | [Curve sketching guide](/blog/curve-sketching-with-derivatives) |
| The Fundamental Theorem | [FTC part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [FTC guide](/blog/fundamental-theorem-of-calculus) |
| Techniques of integration | [Integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts), [partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Trig substitution](/blog/trig-substitution) |
| Improper integrals | [Infinite discontinuities](/learn/calculus-2/improper-integrals-and-applications/infinite-discontinuities) | [Improper integrals guide](/blog/improper-integrals) |
| Areas of planar regions | [Area between curves](/learn/calculus-1/applications-of-integrals/area-between-curves) | [Area between curves guide](/blog/area-between-curves) |
| Power series | [Power series and radius](/learn/calculus-2/power-series-parametric-polar/power-series-and-radius) | [Power series guide](/blog/power-series) |
| Taylor's theorem and Taylor series | [Estimating with Taylor](/learn/calculus-2/power-series-parametric-polar/estimating-with-taylor) | [Taylor's theorem](/theorems/taylors-theorem), [Taylor series](/blog/taylor-series) |

## MATH 275 and the other UCalgary courses

| Course | Title | Relation to MATH 275 |
| --- | --- | --- |
| [MATH 265](/courses/university-of-calgary-math-265) | University Calculus I | Antirequisite (credit for both not allowed) |
| MATH 277 | Multivariable Calculus for Engineers and Scientists | Next course, needs MATH 275 and MATH 211 |
| [MATH 267](/courses/university-of-calgary-math-267) | University Calculus II | Also accepts MATH 275 as a prerequisite |

## Example problems at the MATH 275 level

**1. Optimization.** A box with a square base and no top must hold $32$ cm³. Minimise the surface area $S = x^2 + \frac{128}{x}$. Then $S'(x) = 2x - \frac{128}{x^2} = 0$ gives $x = 4$ cm and height $2$ cm.

**2. Trig substitution.** With $x = \sin\theta$:

$$\int \frac{dx}{\sqrt{1 - x^2}} = \arcsin x + C$$

**3. Taylor's theorem.** Using $\cos x \approx 1 - \frac{x^2}{2}$ for $x = 0.2$ gives $0.98$, and the error is at most $\frac{(0.2)^4}{24} \approx 0.00007$.

## How to do well in MATH 275

- **Expect a fast pace.** Three big topics share one term, so start practising each one in the week it is taught.
- **Use all three contact hours.** Lectures, the tutorial and the extra 1.5-hour block are where most students get help.
- **Make a technique flowchart.** Substitution, parts, trig substitution and partial fractions each have a recognisable shape. Mixed practice in [choosing a strategy](/learn/calculus-2/integration-techniques/choosing-a-strategy) helps.
- **Read applications slowly.** Engineering-style problems often hide the function you must optimize or integrate in the wording.

> **Tip:** for any optimization problem, check the endpoints of the domain as well as the critical points before you choose the answer.

## Frequently asked questions

### What is MATH 275 at the University of Calgary?

MATH 275 is Calculus for Engineers and Scientists. The calendar describes an extensive treatment of single variable differential and integral calculus with an emphasis on applications: derivative laws, the Mean Value Theorem, optimization and curve sketching; the Fundamental Theorem, techniques of integration, improper integrals and areas of planar regions; and power series, Taylor's theorem and Taylor series.

### Is MATH 275 the same as MATH 265?

No, and you cannot get credit for both. MATH 275 includes integration techniques and Taylor series, which MATH 265 leaves for MATH 267, while MATH 265 includes an introduction to several variables.

### What comes after MATH 275?

MATH 277, Multivariable Calculus for Engineers and Scientists, which needs MATH 275 and MATH 211. Students who switch paths can also take MATH 267, which accepts MATH 275 as a prerequisite.

### What should I review before MATH 275?

Math 30-1 and Math 31, especially derivative rules, trig identities and logarithms. The course moves quickly into integration and series.