# Concordia MATH 203 Calculus I: Syllabus, Topics and Practice

> A study guide for Concordia MATH 203 (Differential and Integral Calculus I): limits, derivative rules, related rates, optimization and graphing.

Source: https://practicecalculus.com/courses/concordia-math-203
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 203
- **Credits:** 3 (lecture and tutorial)
- **Prerequisites:** MATH 201 or equivalent
- **Note:** Students in BSc programs or the BA programs in Mathematics and Statistics may not count it toward their program of concentration
- **Covers:** Functions and limits, the derivative as rate of change, derivatives of power, exponential, log and trig functions, product, quotient and chain rules, implicit differentiation, higher derivatives, linearization, related rates, optimization, graphing
- **Next course:** MATH 205 (Differential and Integral Calculus II)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 203 is a 3-credit Differential and Integral Calculus I course at Concordia, with lectures and tutorials.
- Despite its name, it is a differential calculus course: limits, derivative rules and applications.
- Integration starts in the follow-up course, MATH 205.
- It needs MATH 201 or equivalent, and is often required for Extended Credit Program and computer science students.

**MATH 203** is Differential and Integral Calculus I at Concordia University in Montreal, the first of two connected calculus courses. It is the calculus course many students take to complete a prerequisite, for example in the Extended Credit Program or before computer science and engineering courses. This guide maps every MATH 203 topic to free practice so you can learn each idea by solving problems with instant feedback.

## What Concordia MATH 203 covers

The Concordia undergraduate calendar describes MATH 203 as an overview of functions and limits; the derivative as rate of change; differentiation of elementary functions (power, exponential, logarithmic, trigonometric); differentiation rules (product, quotient and chain rules); implicit differentiation; higher derivatives; and approximations using linearization and the differential. Applications include related rates, optimization, analysis of functions (maxima, minima and inflection points) and graphing. It is a 3-credit course with lectures and tutorials, and the prerequisite is MATH 201 or equivalent.

Compared with a typical **Calculus 1**, MATH 203 covers the differential half only. Antiderivatives, definite integrals and the Fundamental Theorem of Calculus are all in MATH 205.

## MATH 203 topic map

| MATH 203 topic | Practice | Read |
| --- | --- | --- |
| Functions | [Function notation](/learn/calculus-1/functions-warmup/function-notation) | [Exponential functions](/functions/exponential-functions), [logarithmic functions](/functions/logarithmic-functions) |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| The derivative as rate of change | [Instantaneous rate of change](/learn/calculus-1/the-derivative/instantaneous-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Power rule | [Power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/rules/power-rule) |
| Exponential, log and trig derivatives | [Exponential and log derivatives](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives), [trig derivatives](/learn/calculus-1/derivative-rules/trig-derivatives) | [Derivatives of exp and log](/blog/derivatives-of-exponential-and-logarithmic-functions) |
| Product, quotient and chain rules | [Product rule](/learn/calculus-1/derivative-rules/product-rule), [chain rule](/learn/calculus-1/derivative-rules/chain-rule-general) | [Product and quotient rules](/blog/product-and-quotient-rules), [chain rule guide](/blog/chain-rule) |
| Implicit differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Implicit differentiation rule](/rules/implicit-differentiation) |
| Higher derivatives | [Second derivative](/learn/calculus-1/applications-of-derivatives/second-derivative) | |
| Linearization and differentials | [Tangent lines at work](/learn/calculus-1/applications-of-derivatives/linear-approximation-and-mvt) | [Linear approximation](/blog/linear-approximation) |
| Related rates | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates guide](/blog/related-rates) |
| Optimization | [Optimization](/learn/calculus-1/applications-of-derivatives/optimization) | [Optimization problems](/blog/optimization-problems) |
| Maxima, minima, inflection, graphing | [Critical points](/learn/calculus-1/applications-of-derivatives/critical-points), [absolute extrema](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Curve sketching](/blog/curve-sketching-with-derivatives) |

## MATH 203 in the Concordia sequence

| Course | Title | Main focus |
| --- | --- | --- |
| MATH 203 | Differential and Integral Calculus I | Limits and derivatives |
| [MATH 205](/courses/concordia-math-205) | Differential and Integral Calculus II | Integrals and series |
| [MAST 218](/courses/concordia-mast-218) | Multivariable Calculus I | Several variables (needs MATH 204 and 205) |

## Example problems at the MATH 203 level

**1. Implicit differentiation.** For $x^2 + y^2 = 25$, differentiate both sides: $2x + 2yy' = 0$, so $y' = -\frac{x}{y}$. At $(3, 4)$ the slope is $-\frac{3}{4}$.

**2. Related rates.** A circle's radius grows at $2$ cm/s. With $A = \pi r^2$, $\frac{dA}{dt} = 2\pi r\frac{dr}{dt}$, so when $r = 5$ the area grows at $20\pi$ cm²/s.

**3. Linearization.** Near $x = 4$, $\sqrt{x} \approx 2 + \frac{1}{4}(x - 4)$, so $\sqrt{4.1} \approx 2.025$.

**4. Inflection points.** For $f(x) = x^3 - 3x$, $f''(x) = 6x$ changes sign at $x = 0$, so $(0, 0)$ is an inflection point.

## How to do well in MATH 203

- **Refresh MATH 201 skills.** Functions, exponents, logs and trig identities appear in every derivative. Our [warm-up practice](/learn/calculus-1/functions-warmup/warmup-practice) is a quick check.
- **Practise rules in mixed sets.** Exams combine the product, quotient and chain rules in one problem.
- **Follow a recipe for word problems.** Draw, name variables, write the equation, differentiate, then substitute numbers last.
- **Use your tutorial.** The calendar lists a tutorial component, which is the best place to get unstuck.

> **Tip:** in related rates, substitute the given numbers only after you differentiate. Plugging in too early turns variables into constants.

## Frequently asked questions

### What is MATH 203 at Concordia?

MATH 203 is Differential and Integral Calculus I, the first of two connected calculus courses. The Concordia calendar lists an overview of functions and limits; the derivative as rate of change; differentiation of power, exponential, logarithmic and trigonometric functions; the product, quotient and chain rules; implicit differentiation; higher derivatives; linearization and the differential; related rates, optimization, analysis of functions and graphing.

### Does MATH 203 cover integrals?

No. Although it is called Differential and Integral Calculus I, the calendar description is all differential calculus. Definite integrals, antiderivatives and the Fundamental Theorem are in MATH 205.

### What is the prerequisite for MATH 203?

MATH 201 or equivalent. Students who already have credit for higher courses such as MAST 218 or MATH 251 may not take it for credit.

### Can BSc students take MATH 203?

The calendar notes that students in programs leading to the BSc, or the BA programs in Mathematics and Statistics, may not apply it to their program of concentration. It is often taken as a prerequisite course, for example in the Extended Credit Program.