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

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 and the other first-year options

After MATH 1A03, continue to 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.

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.