UCalgary MATH 267 University Calculus II: Topics and Practice

MATH 267 is University Calculus II at the University of Calgary. The calendar calls it a concluding treatment of single variable calculus and an introduction to calculus in several variables, which means it packs parts of a usual Calculus 2 and Calculus 3 into one term. This guide maps each MATH 267 topic to free practice so you can keep up with the pace one short lesson at a time.

What UCalgary MATH 267 covers

The University of Calgary calendar lists two blocks. Single variable calculus: techniques of integration, sequences, series, convergence tests and Taylor series. Calculus of several variables: partial differentiation, multiple integration, parametric equations and applications. The course is worth 3 units with 3 hours of lecture and 1 hour of tutorial per week, and needs 3 units from MATH 249, 265 or 275.

Compared with the usual split, MATH 267 is the core of Calculus 2 (techniques and series) plus the start of Calculus 3 (partial derivatives and multiple integrals). Because MATH 265 already covered improper integrals and applications of integration, MATH 267 can move quickly.

MATH 267 topic map

MATH 267 in the UCalgary sequence

Engineering students usually go from MATH 275 to MATH 277 instead of MATH 267.

Example problems at the MATH 267 level

1. Partial fractions.

2. A p-series. \sum \frac{1}{n^2} converges because p = 2 > 1, while the harmonic series \sum \frac{1}{n} diverges.

3. A Maclaurin series. \frac{1}{1 - x} = 1 + x + x^2 + \cdots for |x| < 1. Integrating gives -\ln(1 - x) = x + \frac{x^2}{2} + \frac{x^3}{3} + \cdots.

4. A double integral.

How to do well in MATH 267

• Front-load integration practice. The first weeks set the pace. Mixed sets like choosing a strategy make the technique choice automatic.
• Learn which test fits which series. Geometric and p-series for comparison, ratio test for factorials and powers, alternating series test for alternating signs.
• Switch modes on purpose. When the course turns to several variables, slow down and draw the regions.
• Use tutorials for the hard step. Bring the problems where you could not decide how to begin.

Tip: to set up a double integral, decide the order first, then read the bounds off a sketch from the outside variable in.