# IU MATH-M 211 Calculus I: Syllabus, Topics and Practice

> A study guide for Indiana University Bloomington MATH-M 211 Calculus I: limits, continuity, derivatives and integrals, with practice.

Source: https://practicecalculus.com/courses/indiana-university-math-m211
Updated: 2026-11-08

## At a glance

- **Course code:** MATH-M 211
- **Credits:** 4
- **Prerequisites:** Not listed on the IU course page; check the IU Bloomington math placement exam
- **Covers:** Limits, continuity, derivatives, definite and indefinite integrals, applications to optimization, rates of change and area
- **Offered by:** College of Arts and Sciences, IU Bloomington
- **Next course:** MATH-M 212 Calculus II
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH-M 211 is the 4-credit Calculus I course at Indiana University Bloomington.
- It covers limits, continuity, derivatives, definite and indefinite integrals, and applications to optimization, rates of change and area.
- The math department calls it a gateway course to most sciences, with the Fundamental Theorem of Calculus as its capstone.
- It leads to MATH-M 212 Calculus II and then MATH-M 311 Calculus 3.

**IU MATH-M 211** (Calculus I) is the first calculus course at Indiana University Bloomington, offered by the College of Arts and Sciences. It is worth 4 credits and is the start of the M211, M212, M311 sequence. This guide maps each M211 topic to a short lesson you can practice with instant feedback.

## What IU MATH-M 211 covers

IU's official course listing describes MATH-M 211 as: limits, continuity, derivatives, definite and indefinite integrals, applications. The Department of Mathematics gives a slightly longer version: limits, continuity, derivatives, definite and indefinite integrals, and applications to optimization, rates of change and area. It calls M211 a gateway course to most sciences and many other quantitative areas, and says the Fundamental Theorem of Calculus, which links differentiation with integration, is the capstone of the course.

That is a standard **Calculus 1** course and matches the PracticeCalculus Calculus 1 path from limits through integrals. The official listings do not include a schedule, textbook or prerequisite, so check your section syllabus and placement result for those.

## MATH-M 211 topic map

| M211 topic | Practice | Read |
| --- | --- | --- |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [What is a limit?](/blog/what-is-a-limit) |
| Evaluating limits | [Direct substitution](/learn/calculus-1/limits/direct-substitution) | [How to evaluate limits](/blog/how-to-evaluate-limits) |
| Continuity | [Continuity](/learn/calculus-1/limits/continuity) | [Continuity](/blog/continuity) |
| Derivatives | [Limit definition](/learn/calculus-1/the-derivative/limit-definition) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Derivative rules | [Power rule practice](/learn/calculus-1/derivative-rules/power-rule-practice) | [Power rule](/blog/power-rule) |
| Chain rule | [Chain rule with powers](/learn/calculus-1/derivative-rules/chain-rule-powers) | [Chain rule](/blog/chain-rule) |
| Rates of change | [Related rates](/learn/calculus-1/applications-of-derivatives/related-rates) | [Related rates](/blog/related-rates) |
| Optimization | [Absolute extrema](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Optimization problems](/blog/optimization-problems) |
| Indefinite integrals | [Antiderivative practice](/learn/calculus-1/integrals/antiderivative-practice) | [Antiderivatives](/blog/antiderivatives) |
| Definite integrals and area | [Signed area](/learn/calculus-1/integrals/signed-area) | [Riemann sums](/blog/riemann-sums) |
| Fundamental Theorem of Calculus | [Fundamental Theorem, part 1](/learn/calculus-1/integrals/fundamental-theorem-part-1) | [Fundamental Theorem](/blog/fundamental-theorem-of-calculus) |
| Substitution | [u-substitution](/learn/calculus-1/integrals/u-substitution) | [u-substitution](/blog/u-substitution) |

## M211 in the IU Bloomington sequence

| Course | Credits | Covers |
| --- | --- | --- |
| MATH-M 211 Calculus I | 4 | Limits, derivatives, integrals, applications |
| [MATH-M 212 Calculus II](/courses/indiana-university-math-m212) | 4 | Integration techniques, improper integrals, applications, series |
| [MATH-M 311 Calculus 3](/courses/indiana-university-math-m311) | 3 to 5 | Several variables, partial derivatives, multiple integrals |

## Why M211 matters

The math department calls M211 a gateway course to most sciences and many other quantitative areas, so check whether your major lists it as a requirement. The skills you build here, reading a rate of change from a graph, setting up an optimization problem and computing an area with an integral, come back in physics, statistics and every later math course. Treat it as a foundation, not a box to tick.

## Example problems at the M211 level

**1. Continuity.** For $f(x) = \frac{x^2 - 4}{x - 2}$, the limit as $x \to 2$ is $4$, so defining $f(2) = 4$ makes $f$ continuous.

**2. A rate of change.** If $s(t) = t^3 - 6t$ is position, the velocity at $t = 2$ is

$$s'(2) = 3(2)^2 - 6 = 6$$

**3. The Fundamental Theorem of Calculus.**

$$\frac{d}{dx}\int_1^x \sqrt{t^2 + 1}\,dt = \sqrt{x^2 + 1}$$

## How to do well in MATH-M 211

- **Take the placement exam seriously,** so you start in a course that fits your preparation.
- **Practice a little every day.** Short daily sets like [limits practice](/learn/calculus-1/limits/limits-practice) work better than long weekend sessions.
- **Learn the derivative rules early,** since everything after week five depends on them.
- **Connect derivatives and integrals.** The Fundamental Theorem is the capstone, so make sure you can explain it in words, not just use it.
- **Use the IU Math Learning Center** and our timed [practice exams](/practice) before exams.

> **Tip:** an indefinite integral always needs $+\,C$. Losing it is one of the most common ways to drop points.

## Frequently asked questions

### What is MATH-M 211 at Indiana University?

MATH-M 211 Calculus I is the first course in the IU Bloomington calculus sequence. IU lists it as limits, continuity, derivatives, definite and indefinite integrals, and applications. The math department adds applications to optimization, rates of change and area, and calls the Fundamental Theorem of Calculus the capstone of the course.

### How many credits is MATH-M 211?

IU lists MATH-M 211 at 4 credits.

### What do I need before MATH-M 211?

The IU course page does not print a prerequisite. The math department uses placement exams, so take the IU math placement exam and talk to your advisor about whether you are ready for M211.

### Is MATH-M 211 offered online?

The math department mentions a permission form for a fully online section of MATH-M 211. Availability changes by term, so check the schedule of classes.

### What comes after MATH-M 211?

MATH-M 212 Calculus II, which covers integration techniques, improper integrals, applications such as volume and work, and infinite series.