Ohio State MATH 1131 Calculus for Business: Study Guide, Practice

Ohio State MATH 1131, Calculus for Business, is Ohio State's calculus course with applications to business. It is a 5-credit course offered in autumn and spring, and it surveys calculus of one and several variables with applications to business. This guide maps each MATH 1131 topic to practice with instant feedback.

What Ohio State MATH 1131 covers

The catalog description is a single line: a survey of calculus of one and several variables, applied to business. The department's course description document lists the topics in order.

The first part covers limits and continuity, the derivative and its rules, rates of change, the product, quotient and chain rules, and derivatives of exponential and logarithmic functions. Then come implicit and logarithmic differentiation, higher-order derivatives, differentials, local and absolute extrema, concavity, the second-derivative test, asymptotes, graphing and applied max/min problems.

The integral part covers indefinite integrals, initial conditions, approximating area, the definite integral, the Fundamental Theorem, substitution, area between curves, and consumers' and producers' surplus. It ends with differential equations and partial derivatives, including applications and higher-order partials.

So MATH 1131 covers the core of Calculus 1 plus a short taste of Calculus 3 (partial derivatives).

MATH 1131 topic map

MATH 1131 vs MATH 1151

MATH 1131 is not open to students with credit for MATH 1151 or above. If you may switch to a science or engineering major, see the MATH 1151 guide.

Example problems at the MATH 1131 level

1. Continuous growth. If A(t) = 1000e^{0.05t} dollars, then A'(t) = 50e^{0.05t}. At t = 0 the balance grows at 50 dollars per year.

2. Minimizing average cost. With C(x) = 2x^2 + 50, the average cost is \bar{C}(x) = 2x + \frac{50}{x}. Then \bar{C}'(x) = 2 - \frac{50}{x^2} = 0 gives x = 5, and \bar{C}''(x) = \frac{100}{x^3} > 0, so x = 5 is a minimum with \bar{C}(5) = 20.

3. Partial derivatives of a production function. For P(L, K) = 10L^{0.5}K^{0.5},

At L = 4, K = 9: P_L = 5 \cdot \frac{3}{2} = 7.5, the marginal product of labor.

How to do well in Ohio State MATH 1131

• Master exponential and log derivatives. Growth, interest and logarithmic differentiation all depend on them. Start with exponential functions.
• Always confirm a max or min. Use the second-derivative test or check endpoints, as in the critical points lesson.
• Do not leave partial derivatives for last. They come at the end of the term, right before the final. The idea is simple: treat the other variable as a constant.
• Use the sample exams on the course page, timed practice exams, and the formula sheet. Review common calculus mistakes before each test.

Tip: consumers' surplus is the area between the demand curve and the price line, from zero to the market quantity. Draw it before you integrate.