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

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 vs MATH 221

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 and the MATH 222 guide 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 and 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, such as treating the derivative of e^{2x} as e^{2x}.
• Keep the formula sheet next to you while practicing, and take timed 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 to a business formula.