Queen's MATH 120 Differential and Integral Calculus: Topics Guide

MATH 120 is Differential and Integral Calculus at Queen's University for students who plan to major in Mathematics, Statistics or Physics. It is a full-year, 6.00-unit course, and the calendar describes it as a thorough discussion of calculus. Compared with MATH 121, it puts more weight on understanding and reasoning, and it includes sequences and series. This guide maps every MATH 120 topic to free practice.

What Queen's MATH 120 covers

The Queen's Arts and Science calendar lists the content as a thorough discussion of calculus, including limits, continuity, differentiation, integration, multivariable differential calculus, and sequences and series. Learning hours are 288: 72 lecture, 24 tutorial and 192 private study. There is no formal prerequisite, and MHF4U and MCV4U, 4U AFIC, or permission of the Department are recommended.

The listed learning outcomes go beyond computing. Students should use the ideas fluently in new situations, write clear and well-reasoned mathematical arguments, understand the standards for such arguments, work through harder problems, and master the concepts of limits, continuity, differentiation, integration and convergence. In standard terms, MATH 120 is Calculus 1 and Calculus 2 together, with an introduction to several variables and a more rigorous style.

MATH 120 topic map

MATH 120 vs MATH 121

After MATH 120, students often continue to MATH 280 (Advanced Calculus), MATH 281 (Introduction to Real Analysis) or MATH 221 (Vector Calculus).

Example problems at the MATH 120 level

1. A careful limit. Since |\sin x| \le 1, we have \left|\frac{\sin x}{x}\right| \le \frac{1}{|x|}, so \lim_{x\to\infty}\frac{\sin x}{x} = 0 by the squeeze theorem.

2. An inequality from the MVT. For x > 0, applying the MVT to \ln on [1, 1 + x] gives \ln(1 + x) = \frac{x}{c} for some c in (1, 1 + x), so \frac{x}{1 + x} < \ln(1 + x) < x.

3. A Riemann sum limit.

4. Convergence. \sum \frac{1}{n^p} converges exactly when p > 1, which you can prove with the integral test.

How to do well in MATH 120

• Aim for understanding, not only answers. The learning outcomes ask you to use ideas in new situations, so practise explaining why each step works.
• Write arguments in sentences. State definitions and theorems as you use them. Clear writing is assessed.
• Keep computation sharp. Fluent derivatives and integrals leave time and attention for the harder reasoning problems.
• Expect to struggle productively. The calendar mentions problems that may seem confusing at first. Start early and come back to them.

Tip: when a problem asks you to show an inequality, think of the Mean Value Theorem or a monotonicity argument first.