# McMaster MATH 1A03 Calculus for Science I: Topics and Practice

> A study guide for McMaster MATH 1A03 (Calculus for Science I): limits, derivatives, optimization, curve sketching and integration, with practice.

Source: https://practicecalculus.com/courses/mcmaster-math-1a03
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 1A03
- **Units:** 3 (three lectures and one tutorial, one term)
- **Prerequisites:** One of Grade 12 Calculus and Vectors U, MATH 1F03 or MATH 1MM3
- **Antirequisites:** ARTSSCI 1D06 A/B, MATH 1LS3, 1N03, 1X03, 1Z04, 1ZA3
- **Restrictions:** Not open to students with at least B- in MATH 1M03, students in Mathematics and Statistics I or Engineering, or with credit or registration in ISCI 1A24 A/B
- **Covers:** Limits, continuity, derivatives, optimization, curve sketching, antiderivatives, the definite integral, techniques of integration
- **Next course:** MATH 1AA3 (Calculus for Science II)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 1A03 is McMaster's 3-unit Calculus for Science I, aimed at science students and geared towards applications.
- It covers limits, continuity, derivatives, optimization and curve sketching.
- It also covers antiderivatives, the definite integral and techniques of integration.
- Engineering students take MATH 1ZA3 instead, and MATH 1AA3 is the next course.

**MATH 1A03** is Calculus for Science I at McMaster University in Hamilton. It is the first calculus course for most students in the Faculty of Science, and the calendar describes it as geared towards applications with attention to underlying concepts. In one term it covers derivatives and their uses, then the basics of integration. This guide maps every MATH 1A03 topic to free practice so you can learn each idea by solving problems.

## What McMaster MATH 1A03 covers

The McMaster undergraduate calendar lists the topics as limits, continuity, derivatives, optimization, curve sketching, antiderivatives, the definite integral and techniques of integration. The format is three lectures and one tutorial a week for one term, and the course is worth 3 units. The prerequisite is one of Grade 12 Calculus and Vectors U, MATH 1F03 or MATH 1MM3.

The link above points to the 2025-2026 calendar entry, the most recent individual course page we could confirm. Check the current McMaster calendar for any changes.

This is a standard **Calculus 1** course. The calendar does not say which integration techniques are included, so check your course outline; substitution is always part of a first course, and some sections go further.

## MATH 1A03 topic map

| MATH 1A03 topic | Practice | Read |
| --- | --- | --- |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit), [one-sided and infinite limits](/learn/calculus-1/limits/one-sided-and-infinite-limits) | [How to evaluate limits](/blog/how-to-evaluate-limits), [limit laws](/rules/limit-laws) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity guide](/blog/continuity), [IVT](/theorems/intermediate-value-theorem) |
| The derivative | [The limit definition](/learn/calculus-1/the-derivative/limit-definition), [tangent lines](/learn/calculus-1/the-derivative/tangent-lines) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Derivative rules | [Mixed rules practice](/learn/calculus-1/derivative-rules/derivative-rules-practice) | [Power rule](/rules/power-rule), [chain rule](/rules/chain-rule) |
| Implicit and log differentiation | [Implicit differentiation](/learn/calculus-1/derivative-rules/implicit-differentiation) | [Logarithmic differentiation](/rules/logarithmic-differentiation) |
| 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) |
| Antiderivatives | [Undoing derivatives](/learn/calculus-1/integrals/undoing-derivatives), [reverse power rule](/learn/calculus-1/integrals/reverse-power-rule) | [Antiderivatives guide](/blog/antiderivatives) |
| The definite integral | [Riemann sums](/learn/calculus-1/integrals/riemann-sums), [FTC part 2](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [FTC guide](/blog/fundamental-theorem-of-calculus) |
| Techniques of integration | [u-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution guide](/blog/u-substitution), [integration by parts](/blog/integration-by-parts) |

## MATH 1A03 and the other first-year options

| Course | Title | Who it is for |
| --- | --- | --- |
| MATH 1A03 | Calculus for Science I | Science students |
| MATH 1ZA3 | Engineering Mathematics I | Engineering students (an antirequisite of 1A03) |
| MATH 1LS3 | Another first calculus course | Also an antirequisite of 1A03 |

After MATH 1A03, continue to [MATH 1AA3](/courses/mcmaster-math-1aa3).

## Example problems at the MATH 1A03 level

**1. A one-sided limit.** $\lim_{x\to 0^+}\frac{1}{x} = \infty$ but $\lim_{x\to 0^-}\frac{1}{x} = -\infty$, so the two-sided limit does not exist.

**2. Optimization.** A farmer has $200$ m of fence for a rectangle along a river (no fence on the river side). With area $A = x(200 - 2x)$, $A'(x) = 200 - 4x = 0$ gives $x = 50$ m and a maximum area of $5000$ m².

**3. Curve sketching.** For $f(x) = xe^{-x}$, $f'(x) = (1 - x)e^{-x}$, so $f$ increases on $(-\infty, 1)$ and decreases on $(1, \infty)$, with a maximum at $x = 1$.

**4. The definite integral.**

$$\int_1^e \frac{1}{x}\,dx = \ln e - \ln 1 = 1$$

## How to do well in MATH 1A03

- **Use your tutorial every week.** The calendar lists one tutorial a week. Bring questions you could not start.
- **Practise applications, not only rules.** The course is geared towards applications, so optimization and curve sketching carry real weight.
- **Keep concepts in view.** Know what a derivative means as a rate and a slope, not just how to compute one.
- **Review Grade 12 Calculus and Vectors.** The first weeks move quickly through limits and derivative rules you have seen before.

> **Tip:** in optimization, write the quantity to maximise as a function of one variable before you differentiate. Use the constraint to remove the other variable.

## Frequently asked questions

### What is MATH 1A03 at McMaster?

MATH 1A03 is Calculus for Science I. The McMaster calendar describes it as a course for science students, geared towards applications with attention to underlying concepts. Topics are limits, continuity, derivatives, optimization, curve sketching, antiderivatives, the definite integral and techniques of integration.

### What do I need for MATH 1A03?

One of Grade 12 Calculus and Vectors U, MATH 1F03 or MATH 1MM3.

### Who cannot take MATH 1A03?

The calendar says it is not open to students with at least B- in MATH 1M03, students in Mathematics and Statistics I or an Engineering program, or students with credit or registration in ISCI 1A24 A/B. MATH 1ZA3 (Engineering Mathematics I) and MATH 1LS3 are among its antirequisites.

### What comes after MATH 1A03?

MATH 1AA3, Calculus for Science II, which covers more integration techniques, differential equations, polar and parametric curves, series, partial derivatives and double integrals.