UCalgary MATH 265 University Calculus I: Topics and Practice

MATH 265 is University Calculus I at the University of Calgary. The calendar describes it as an introduction to single variable calculus for students who already have credit in high school calculus, so it moves at a confident pace. It covers derivatives and integrals in one term, adds improper integrals, and even gives a first look at calculus in several variables. This guide maps each MATH 265 topic to free practice so you can learn by solving problems.

What UCalgary MATH 265 covers

The University of Calgary calendar says limits, derivatives and integrals of algebraic, exponential, logarithmic and trigonometric functions play a central role. Additional topics include applications of differentiation; the Fundamental Theorem of Calculus, improper integrals and applications of integration. Differential calculus in several variables is also introduced. The course is worth 3 units, with 3 hours of lecture and 1 hour of tutorial a week.

This is a full Calculus 1 course with a few extras. Improper integrals usually belong to Calculus 2, and partial derivatives usually belong to Calculus 3, so MATH 265 previews both.

MATH 265 topic map

First calculus options at UCalgary

After MATH 265, continue to MATH 267. If you are in engineering, see MATH 275 instead.

Example problems at the MATH 265 level

1. L'Hopital's rule.

2. FTC part 1. If G(x) = \int_1^x \ln t\,dt, then G'(x) = \ln x.

3. An improper integral. \int_1^\infty \frac{1}{x}\,dx = \lim_{b\to\infty}\ln b = \infty, so it diverges, while \int_1^\infty \frac{1}{x^2}\,dx = 1 converges.

4. A first partial derivative. For f(x, y) = x^3y^2, f_x = 3x^2y^2 and f_y = 2x^3y.

How to do well in MATH 265

• Use what you know from Math 31. The course assumes you have seen calculus, so review derivative rules in the first week rather than waiting.
• Go to your tutorial. The (3-1) hours mean a weekly tutorial, the best place to ask about the first step of a problem.
• Connect derivatives and integrals. Check every antiderivative by differentiating it.
• Do not skip the new material at the end. Improper integrals and partial derivatives are short units, but they are on the final.

Tip: a \frac{0}{0} or \frac{\infty}{\infty} form is required before you use L'Hopital's rule. Check the form first.