Purdue MA 16010 Applied Calculus I: Study Guide and Practice

Purdue MA 16010, Applied Calculus I, is Purdue's applied first calculus course for students in the life, managerial and social sciences. It carries 3 credit hours and is followed by MA 16020, Applied Calculus II. This guide maps every MA 16010 topic to practice with instant feedback.

What Purdue MA 16010 covers

The math department lists the topics: trigonometric and exponential functions; limits and differentiation and the rules of differentiation; maxima, minima and optimization; curve sketching; integration, antiderivatives and the Fundamental Theorem of Calculus; and properties of definite integrals and numerical methods. Applications come from the life, managerial and social sciences.

That covers the core of a standard Calculus 1 course with an applied focus. It starts with a review of the functions you will differentiate, which is why our matching path begins with the functions warm-up.

MA 16010 topic map

MA 16010 and the applied sequence

If your plans change toward engineering or the physical sciences, compare the MA 16500 guide and the MA 16100 guide.

Example problems at the MA 16010 level

1. Population growth. A bacteria population is P(t) = 200e^{0.3t}. Its growth rate is P'(t) = 60e^{0.3t}, so at t = 0 it grows by 60 bacteria per hour.

2. Optimization. A farmer has 400 m of fence for a rectangular pen against a barn wall (no fence needed on that side). With width x, the area is A(x) = x(400 - 2x). Then A'(x) = 400 - 4x = 0 gives x = 100, so the pen is 100 m by 200 m with area 20{,}000 m².

3. A left Riemann sum. Estimate \int_0^2 x^2\,dx with 2 rectangles of width 1, using left endpoints:

The exact value is \frac{8}{3} \approx 2.67, so the left sum underestimates for this increasing function.

How to do well in Purdue MA 16010

• Get comfortable with e^x early. Growth and decay models appear throughout the course. Start with exponential functions.
• Set up word problems carefully. Draw a picture, name the variables and write the function before differentiating, as in the optimization guide.
• Understand what an integral estimates. Riemann sums make the definite integral concrete. See the Riemann sums guide.
• Use the formula sheet and timed practice exams, and review common calculus mistakes before exams.

Tip: for an increasing function, left Riemann sums underestimate and right sums overestimate. Knowing that lets you check your numbers quickly.