Purdue MA 16500 Calculus I: Topics, Study Guide and Practice

Purdue MA 16500, Analytic Geometry And Calculus I, is the first calculus course for Purdue students who already saw some calculus in high school. It carries 4 credit hours and leads into MA 16600 and then MA 26100. This guide maps every MA 16500 topic to practice with instant feedback, so you can sharpen each skill by solving problems.

What Purdue MA 16500 covers

The math department describes MA 16500 as an introduction to differential and integral calculus of one variable with applications, plus conic sections. It is designed for students with at least one semester of high school calculus earning an A or B who do not place into MA 16200, MA 16600 or the advanced placement courses, and it expects competence in college algebra and trigonometry.

A Purdue Engineering course outline for MA 16500 lists the weekly topics: functions, exponentials and logarithms, limits and continuity, limits at infinity, the derivative, product, quotient and chain rules, trig and log derivatives, implicit differentiation, hyperbolic functions, exponential growth and related rates, linear approximation, max and min values, the Mean Value Theorem, curve shape, L'Hôpital's rule, optimization, and finally antiderivatives, the definite integral, the Fundamental Theorem and substitution.

That is a complete Calculus 1 course, taught at a pace that assumes you have met the ideas before.

MA 16500 topic map

The Purdue calculus sequence

Continue with the MA 16600 guide and the MA 26100 guide. If you are deciding between first courses, see the MA 16100 guide, or the MA 16010 guide for applied calculus.

Example problems at the MA 16500 level

1. A quotient rule derivative. Differentiate f(x) = \frac{x}{x^2 + 1}:

2. Exponential decay. A sample decays as A(t) = 80e^{-0.1t} grams. Its rate of change at t = 0 is A'(0) = -0.1 \cdot 80 = -8 grams per unit time.

3. L'Hôpital's rule. The limit \lim_{x \to 0} \frac{e^x - 1}{x} has the form \frac{0}{0}, so

How to do well in Purdue MA 16500

• Do not coast on high school calculus. The course assumes you have seen the basics and moves on quickly to applications. Fill gaps early with mixed derivative practice.
• Make curve sketching systematic. Use the first and second derivative together, as in the concavity lesson.
• Check your work for algebra errors. The list of common calculus mistakes covers the ones that cost the most points.
• Use the formula sheet while learning, then take timed practice exams before each exam.
• Plan exam prep with how to prepare for a calculus exam.

Tip: L'Hôpital's rule only applies to \frac{0}{0} or \frac{\infty}{\infty} forms. Check the form first, every time.