# UW-Madison MATH 211 Survey of Calculus 1: Study Guide, Practice

> A study guide for MATH 211 at UW-Madison: derivatives, integrals, exponentials, logs and functions of several variables for business students.

Source: https://practicecalculus.com/courses/uw-madison-math-211
Updated: 2026-11-03

## At a glance

- **Course code:** MATH 211
- **Credits:** 4
- **Requisites:** MATH 112, 114 or 171, or placement into MATH 211 or 221; not open to students with credit for MATH 221
- **Covers:** Essential differential and integral calculus, exponential and logarithmic functions, functions of several variables
- **Intended for:** Mainly prebusiness and some social science students
- **Next course:** MATH 213 (Survey of Calculus 2)
- **Practice here:** [Calculus 1](/learn/calculus-1)

## Key takeaways

- MATH 211, Survey of Calculus 1, is a 4-credit calculus course at UW-Madison intended mainly for prebusiness and some social science students.
- It covers the essentials of derivatives and integrals, exponential and logarithmic functions, and an introduction to functions of several variables.
- It is not a substitute for MATH 221: students heading to math, physics, engineering or most biological sciences should take MATH 221.
- The follow-on course is MATH 213, Survey of Calculus 2.

**MATH 211** is Survey of Calculus 1 at the University of Wisconsin-Madison, the calculus course most prebusiness and many social science students take. It is worth 4 credits and focuses on the calculus you need to model costs, revenue and growth, not on the proofs and trig-heavy material of the main sequence. This guide maps every MATH 211 topic to free practice, so you can learn each idea by solving problems with instant feedback.

## What MATH 211 covers

The UW-Madison Guide describes MATH 211 as covering the essential ideas of differential and integral calculus, exponential and logarithmic functions, and functions of several variables. It also notes that students headed for advanced work in math, physics, engineering or most biological sciences should take MATH 221 instead.

Compared with a standard **Calculus 1** course, MATH 211 keeps the core (derivatives, optimization, definite integrals) and leans on exponential and logarithmic models. It also adds a short taste of functions of several variables, such as partial derivatives, which a typical Calculus 1 course leaves for Calculus 3.

## MATH 211 topic map

| MATH 211 topic | Practice | Read |
| --- | --- | --- |
| Rates of change | [Slope and rate of change](/learn/calculus-1/functions-warmup/slope-and-rate-of-change) | [Linear function](/functions/linear-function) |
| Limits | [What is a limit?](/learn/calculus-1/limits/what-is-a-limit) | [What is a limit?](/blog/what-is-a-limit) |
| The derivative | [Average rate of change](/learn/calculus-1/the-derivative/average-rate-of-change) | [Limit definition of the derivative](/blog/limit-definition-of-the-derivative) |
| Derivative rules | [Power rule](/learn/calculus-1/derivative-rules/power-rule) | [Power rule](/blog/power-rule), [product and quotient rules](/blog/product-and-quotient-rules) |
| Exponential and log functions | [Exponentials and logarithms](/learn/calculus-1/derivative-rules/exponential-and-log-derivatives) | [Exponential functions](/functions/exponential-functions), [logarithmic functions](/functions/logarithmic-functions) |
| Chain rule | [Chain rule: e and ln](/learn/calculus-1/derivative-rules/chain-rule-exponentials) | [Chain rule](/rules/chain-rule) |
| Optimization | [Absolute extrema on an interval](/learn/calculus-1/applications-of-derivatives/absolute-extrema) | [Optimization problems](/blog/optimization-problems) |
| Antiderivatives | [The reverse power rule](/learn/calculus-1/integrals/reverse-power-rule) | [Antiderivatives](/blog/antiderivatives) |
| Definite integrals | [Evaluating definite integrals](/learn/calculus-1/integrals/fundamental-theorem-part-2) | [Fundamental Theorem of Calculus](/blog/fundamental-theorem-of-calculus) |
| Net change and average value | [Net change and displacement](/learn/calculus-1/applications-of-integrals/net-change) | [Average value](/learn/calculus-1/applications-of-integrals/average-value) |
| Functions of several variables | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Partial derivatives](/blog/partial-derivatives) |

## MATH 211 vs MATH 221

| | MATH 211 Survey of Calculus 1 | MATH 221 Calculus and Analytic Geometry 1 |
| --- | --- | --- |
| Credits | 4 | 5 |
| Intended for | Prebusiness and some social science students | Math, physics, engineering, most biological sciences |
| Content | Essential calculus, exponentials and logs, several variables | Full single-variable calculus, analytic geometry, transcendental functions |
| Next course | MATH 213 | MATH 222 |

MATH 211 does not satisfy the requisite for MATH 222, and it is closed to students who already have credit for MATH 221. If there is a chance you will switch to a science or engineering major, check with an advisor before choosing. See the [MATH 221 guide](/courses/uw-madison-math-221) and the [MATH 222 guide](/courses/uw-madison-math-222) for the main sequence.

## Example problems at the MATH 211 level

**1. Marginal cost.** If $C(q) = 500 + 20q - 0.1q^2$, the marginal cost is $C'(q) = 20 - 0.2q$. At $q = 50$ units, $C'(50) = 20 - 10 = 10$, so the 51st unit costs about 10 dollars.

**2. Continuous growth.** For $P(t) = 1000e^{0.05t}$, the growth rate is $P'(t) = 50e^{0.05t}$. At $t = 0$ the population grows by 50 per year.

**3. A partial derivative.** For a profit model $f(x, y) = 4x + 6y - x^2 - y^2$, holding $y$ fixed gives $f_x = 4 - 2x$, and holding $x$ fixed gives $f_y = 6 - 2y$. Both are zero at $(2, 3)$, the candidate for the maximum profit.

## How to do well in MATH 211

- **Get fluent with $e^x$ and $\ln x$.** Business models use them constantly. The [natural exponential function](/functions/natural-exponential-function) and [natural logarithm](/functions/natural-logarithm) pages summarize every rule you need.
- **Translate words into functions first.** Most points in applied problems come from setting up cost, revenue or profit correctly. Then the calculus is short.
- **Avoid the classic errors** listed in [common calculus mistakes](/blog/common-calculus-mistakes), such as treating the derivative of $e^{2x}$ as $e^{2x}$.
- **Keep the [formula sheet](/formulas) next to you** while practicing, and take timed [practice](/practice) sets before each exam.

> **Tip:** marginal anything (cost, revenue, profit) just means the derivative. Once that clicks, a large part of MATH 211 is applying the [power rule](/rules/power-rule) to a business formula.

## Frequently asked questions

### What is MATH 211 at UW-Madison?

MATH 211 is Survey of Calculus 1, a one-semester introduction to the essential ideas of differential and integral calculus, exponential and logarithmic functions, and functions of several variables. It is aimed mainly at prebusiness and some social science students.

### Should I take MATH 211 or MATH 221?

The UW-Madison Guide says students preparing for advanced study in mathematics, physics, engineering or most biological sciences should take MATH 221. MATH 211 suits business and some social science programs. MATH 211 is not open to students who already have credit for MATH 221, and it does not satisfy the requisite for MATH 222.

### What comes after MATH 211?

MATH 213, Survey of Calculus 2, which covers first-order differential equations, multivariable calculus with constrained optimization, sequences and series, approximation methods and a short introduction to probability.

### Is MATH 211 easier than MATH 221?

It is a survey course worth 4 credits rather than 5, and it focuses on essential techniques and applications rather than the full theory and trig-heavy material of MATH 221. It still requires steady practice with derivatives and integrals.

### How should I prepare for MATH 211?

Make sure exponent rules, logarithms and linear functions are comfortable, then start on limits and derivatives. The free functions warm-up unit on PracticeCalculus is a good place to begin.