# uOttawa MAT 1320 Calculus I: Syllabus, Topics and Practice

> A study guide for University of Ottawa MAT 1320 (Calculus I): limits, derivatives, optimization, Newton's method, integration and numerical methods.

Source: https://practicecalculus.com/courses/university-of-ottawa-mat-1320
Updated: 2026-11-08

## At a glance

- **Course code:** MAT 1320
- **Units:** 3 (lecture and discussion group)
- **Prerequisites:** One of MAT 1339, Ontario 4U Calculus and Vectors (MCV4U) or an equivalent
- **Credit restriction:** ADM 1305, MAT 1300, 1308, 1320, 1321, 1327, 1329 and 1330 cannot be combined for units
- **Covers:** Limits and continuity, derivative formulas, finite differences, curve analysis, extreme and mean value theorems, L'Hospital's rule, related rates, optimization, Newton's method, the FTC, integration techniques, numerical integration
- **Next course:** MAT 1322 (Calculus II)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MAT 1320 is the 3-unit Calculus I course at the University of Ottawa, taught in English, with lectures and discussion groups.
- It covers limits, derivatives and their applications, including L'Hospital's rule and Newton's method.
- It also covers the definite integral, the Fundamental Theorem, integration by parts, substitution and partial fractions.
- It ends with numerical integration and error analysis, and MAT 1322 comes next.

**MAT 1320** is Calculus I at the University of Ottawa, the English-language first calculus course for science and engineering students who have MCV4U. It covers a lot of ground: the core of differential calculus, then integration with three techniques, and finally numerical integration with error analysis. This guide maps every MAT 1320 topic to free practice so you can learn each idea by solving problems.

## What uOttawa MAT 1320 covers

The uOttawa catalogue lists: intuitive definition of limits; continuity and a statement of the intermediate value theorem; a quick review of basic derivative formulas (products, the chain rule, exponentials and trig functions); derivatives of quotients, logarithms and inverse trig functions; finite difference approximations of derivatives; analysis of functions via the first and second derivatives; statements of the extreme and mean value theorems; L'Hospital's rule; implicit differentiation, related rates, optimization, linear approximation and Newton's method; the definite integral and the Fundamental Theorem of Calculus; antiderivatives of elementary functions and techniques of integration (integration by parts, substitutions, partial fractions); and numerical integration with the midpoint, trapezoidal and Simpson's rules and error analysis.

That is more than a typical **Calculus 1**. Integration by parts and partial fractions usually belong to Calculus 2, and the numerical methods give the course an applied, engineering flavour.

## MAT 1320 topic map

| MAT 1320 topic | Practice | Read |
| --- | --- | --- |
| Limits and continuity | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit), [continuity](/learn/calculus-1/limits/continuity) | [Intermediate Value Theorem](/theorems/intermediate-value-theorem) |
| Derivative formulas | [Mixed rules practice](/learn/calculus-1/derivative-rules/derivative-rules-practice) | [Chain rule](/rules/chain-rule), [quotient rule](/rules/quotient-rule) |
| Log and inverse trig derivatives | [Inverse trig derivatives](/learn/calculus-1/derivative-rules/inverse-trig-derivatives) | [Derivative of ln x](/derivatives/ln-x), [derivative of arcsin x](/derivatives/arcsin-x) |
| Finite difference approximations | [Average rate of change](/learn/calculus-1/the-derivative/average-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Analysis with first and second derivatives | [Increasing and decreasing](/learn/calculus-1/applications-of-derivatives/increasing-and-decreasing), [second derivative](/learn/calculus-1/applications-of-derivatives/second-derivative) | [Curve sketching](/blog/curve-sketching-with-derivatives) |
| Extreme and mean value theorems | [Absolute extrema](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Extreme Value Theorem](/theorems/extreme-value-theorem), [Mean Value Theorem](/theorems/mean-value-theorem) |
| L'Hospital's rule | [L'Hopital's rule](/learn/calculus-1/applications-of-derivatives/lhopitals-rule) | [L'Hopital's rule guide](/blog/lhopitals-rule) |
| Implicit differentiation, related rates | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation), [related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates guide](/blog/related-rates) |
| Optimization, linear approximation, Newton's method | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization), [tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Linear approximation](/blog/linear-approximation) |
| Definite integral and the FTC | [FTC part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [FTC guide](/blog/fundamental-theorem-of-calculus) |
| Integration techniques | [u-substitution](/learn/calculus-1/integrals/u-substitution), [integration by parts](/learn/calculus-2/integration-techniques/integration-by-parts), [partial fractions](/learn/calculus-2/integration-techniques/partial-fractions) | [Integration by parts guide](/blog/integration-by-parts) |
| Numerical integration | [Trapezoid sums](/learn/calculus-1/integrals/trapezoid-sums), [Riemann sums](/learn/calculus-1/integrals/riemann-sums) | [Riemann sums guide](/blog/riemann-sums) |

## MAT 1320 vs MAT 1321

| Course | Title | Prerequisite | Starting point |
| --- | --- | --- | --- |
| MAT 1320 | Calculus I | MCV4U or MAT 1339 | Reviews basic derivative formulas |
| MAT 1321 | Foundations of Calculus I | MHF4U or MAT 1318 | Builds derivatives from limits |

They cannot be combined for units. Either one leads to [MAT 1322](/courses/university-of-ottawa-mat-1322). Engineering students later take [MAT 2322](/courses/university-of-ottawa-mat-2322).

## Example problems at the MAT 1320 level

**1. A finite difference.** For $f(x) = x^3$ at $x = 2$ with $h = 0.1$, the forward difference $\frac{f(2.1) - f(2)}{0.1} = 12.61$ approximates $f'(2) = 12$.

**2. Partial fractions.**

$$\int \frac{dx}{x(x + 1)} = \ln|x| - \ln|x + 1| + C$$

**3. The trapezoidal rule.** With $n = 2$ on $\int_0^2 x^2\,dx$: $\frac{1}{2}\left(0 + 2 \cdot 1 + 4\right) = 3$, compared with the exact value $\frac{8}{3}$.

**4. Newton's method.** For $x^2 - 3 = 0$ from $x_0 = 2$: $x_1 = 2 - \frac{1}{4} = 1.75$, close to $\sqrt{3} \approx 1.732$.

## How to do well in MAT 1320

- **Treat the review as a check.** The basic derivative formulas are only reviewed quickly. If they are not automatic yet, practise them in the first week.
- **Attend discussion groups.** The catalogue lists a discussion group component, the best place to work through problems with help.
- **Know the error behaviour.** For numerical integration, understand why Simpson's rule is usually more accurate than the trapezoidal rule.
- **Mix integration techniques.** Practise choosing between substitution, parts and partial fractions, not just applying each one.

> **Tip:** for the extreme value theorem, a function must be continuous on a closed interval. Always check the endpoints as well as the critical points.

## Frequently asked questions

### What is MAT 1320 at uOttawa?

MAT 1320 is Calculus I. The uOttawa catalogue lists an intuitive definition of limits, continuity and the intermediate value theorem; a review of derivative formulas; derivatives of quotients, logarithms and inverse trig functions; finite difference approximations; analysis of functions with first and second derivatives; the extreme and mean value theorems; L'Hospital's rule; implicit differentiation, related rates, optimization, linear approximation and Newton's method; the definite integral and the Fundamental Theorem; integration techniques; and numerical integration with error analysis.

### MAT 1320 vs MAT 1321?

They cannot be combined for units. MAT 1321, Foundations of Calculus I, needs MHF4U (Advanced Functions) or MAT 1318 and starts from instantaneous rate of change and the definition of limits. MAT 1320 needs MCV4U or MAT 1339 and treats basic derivative formulas as review.

### Do I need MCV4U for MAT 1320?

Yes. The prerequisite is one of MAT 1339, Ontario 4U Calculus and Vectors (MCV4U) or an equivalent.

### What comes after MAT 1320?

MAT 1322, Calculus II, which covers improper integrals, applications of the integral, differential equations, series and an introduction to functions of several variables.