IU MATH-M 212 Calculus II: Syllabus, Topics and Practice

IU MATH-M 212 (Calculus II) is the second calculus course at Indiana University Bloomington, after MATH-M 211. It carries 4 credits and is offered by the College of Arts and Sciences. This guide maps each topic in the official description to lessons you can practice with instant feedback.

What IU MATH-M 212 covers

IU's official course listing describes MATH-M 212 as: techniques of integration (by parts, trigonometric substitutions, partial fractions), improper integrals, volume, work, arclength, surface area, infinite series.

That is a standard Calculus 2 course. The listing is a short summary, so it does not name a textbook, schedule or prerequisite, and it does not say whether power series, Taylor series, parametric curves or polar coordinates are included. Check your section syllabus for those details. An honors version, MATH-S 212 Honors Calculus II, is also offered.

MATH-M 212 topic map

M212 in the IU Bloomington sequence

How M212 builds on M211

M212 assumes you can differentiate quickly and evaluate basic definite integrals with the Fundamental Theorem of Calculus from M211. The first part of the course adds new ways to find antiderivatives. The middle part uses integrals as a tool to measure volumes, lengths, surface areas and work. The last part changes direction and asks when an infinite sum adds up to a finite number, which needs careful use of limits. Students who keep their M211 skills sharp usually find the transition much smoother.

Example problems at the M212 level

1. A trig substitution. With x = \sin\theta:

2. Work. A spring with k = 10 N/m stretched from 0 to 0.5 m:

3. A p-series. \sum_{n=1}^{\infty} \frac{1}{n^2} converges because p = 2 > 1, while \sum_{n=1}^{\infty} \frac{1}{\sqrt{n}} diverges because p = \frac{1}{2} \le 1.

How to do well in MATH-M 212

• Review M211 integrals first. Every new technique ends with a basic antiderivative, so the antiderivative practice lesson is a smart warm-up.
• Practice choosing a technique with mixed sets like choosing a strategy.
• Set up applications from a slice. For volume, work and arclength, write the formula for one thin piece first.
• Give series extra time. Work through choosing a test and convergence tests problems.
• Take timed practice exams and use the IU Math Learning Center when you are stuck.

Tip: an improper integral is a limit. Replace the infinite bound or the bad point with a variable, integrate, then take the limit.