Purdue MA 26100 Multivariate Calculus: Study Guide and Practice

Purdue MA 26100, Multivariate Calculus, is the third course in Purdue's calculus sequence, taken after MA 16600 or MA 16200. It is a 4-credit course that takes calculus into three dimensions. This guide maps every MA 26100 topic to practice with instant feedback.

What Purdue MA 26100 covers

The math department's description is short: planes, lines and curves in three dimensions, differential calculus of several variables, multiple integrals and an introduction to vector calculus. A Purdue Engineering course outline lists the weekly topics.

It starts with 3D coordinates, vectors, dot and cross products, lines and planes, cylinders and quadric surfaces, then vector functions, arc length, curvature and motion in space. Next come functions of several variables, limits, partial derivatives, tangent planes, the chain rule, directional derivatives and the gradient, max and min values and Lagrange multipliers. Integration covers double integrals over rectangles, general regions and in polar coordinates, surface area, triple integrals in cylindrical and spherical coordinates, and change of variables. The course closes with vector fields, line integrals, Green's theorem, curl and divergence, surface integrals, Stokes' theorem and the Divergence Theorem.

That is a complete Calculus 3 course.

MA 26100 topic map

How students reach MA 26100

Both paths meet in MA 26100. See the MA 16600 guide for the prerequisite material and the MA 16500 guide for the start of the sequence.

Example problems at the MA 26100 level

1. A plane through a point. The plane through (1, 0, 2) with normal \langle 2, -1, 3 \rangle is

2. A chain rule. If z = x^2 y with x = t^2 and y = 3t, then

which matches differentiating z = 3t^5 directly.

3. Green's theorem. For \mathbf{F} = \langle -y, x \rangle around the unit circle counterclockwise,

How to do well in Purdue MA 26100

• Picture the geometry. Sketch surfaces and regions before setting up integrals, and practice switching the order to get bounds right.
• Check answers two ways. As in the chain rule example, a second method often catches errors.
• Learn the theorems as one family. Read Green's theorem first, then Stokes' theorem and the Divergence theorem.
• Keep the formula sheet close for coordinate conversions, and take timed practice exams.
• See the big picture in Calculus 1 vs 2 vs 3.

Tip: spherical coordinates need the factor \rho^2 \sin\phi. Forgetting it is the single most common triple integral mistake.