# Purdue MA 26100 Multivariate Calculus: Study Guide and Practice

> A study guide for Purdue MA 26100 (Multivariate Calculus): 3D geometry, partial derivatives, multiple integrals and vector calculus, with free practice.

Source: https://practicecalculus.com/courses/purdue-ma-26100
Updated: 2026-11-03

## At a glance

- **Course code:** MA 26100
- **Credit hours:** 4
- **Prerequisites:** C- or better in MA 16200 or MA 16600, among other accepted courses
- **Covers:** Planes, lines and curves in three dimensions, differential calculus of several variables, multiple integrals, introduction to vector calculus
- **Restrictions:** Not open to students with credit in MA 27100
- **Practice here:** [Calculus 3](/learn/calculus-3)

## Key takeaways

- MA 26100 is Purdue's 4-credit multivariable calculus course.
- It covers lines, planes and curves in 3D, partial derivatives and the gradient, multiple integrals and an introduction to vector calculus.
- Students reach it after MA 16600 or MA 16200 with a C- or better.
- It is not open to students with credit in MA 27100.

**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

| MA 26100 topic | Practice | Read |
| --- | --- | --- |
| Lines and planes | [Lines in space](/learn/calculus-3/vectors-and-space/lines-in-space), [planes in space](/learn/calculus-3/vectors-and-space/planes-in-space) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |
| Vector functions, arc length, motion | [Curves and motion](/learn/calculus-3/vectors-and-space/curves-and-motion) | [Parametric arc length](/learn/calculus-2/power-series-parametric-polar/parametric-arc-length) |
| Functions of several variables | [Functions of several variables](/learn/calculus-3/partial-derivatives/functions-of-several-variables) | [Partial derivatives](/blog/partial-derivatives) |
| Partial derivatives | [Second partial derivatives](/learn/calculus-3/partial-derivatives/second-partial-derivatives) | [Partial derivatives](/blog/partial-derivatives), [Clairaut's theorem](/theorems/clairauts-theorem) |
| Tangent planes and the chain rule | [Tangent planes](/learn/calculus-3/partial-derivatives/tangent-planes) | [Linear approximation](/blog/linear-approximation) |
| Gradient and directional derivatives | [Gradient and directional derivatives](/learn/calculus-3/partial-derivatives/gradient-and-directional-derivatives) | [Gradient and directional derivatives](/blog/gradient-and-directional-derivatives) |
| Max/min and Lagrange multipliers | [Lagrange multipliers](/learn/calculus-3/partial-derivatives/lagrange-multipliers) | [Lagrange multipliers](/blog/lagrange-multipliers) |
| Double integrals and polar | [Double integrals over general regions](/learn/calculus-3/multiple-integrals/general-regions) | [Double integrals](/blog/double-integrals) |
| Triple integrals | [Triple integrals](/learn/calculus-3/multiple-integrals/triple-integrals) | [Double integrals](/blog/double-integrals) |
| Change of variables | [Change of variables and the Jacobian](/learn/calculus-3/multiple-integrals/change-of-variables) | [Double integrals](/blog/double-integrals) |
| Vector fields and line integrals | [Line integrals of functions](/learn/calculus-3/vector-calculus/line-integrals-of-functions) | [Green's theorem](/theorems/greens-theorem) |
| Green's theorem, curl and divergence | [Green's theorem](/learn/calculus-3/vector-calculus/greens-theorem) | [Green's theorem](/theorems/greens-theorem) |
| Surface integrals, Stokes and Divergence | [Stokes and the Divergence Theorem](/learn/calculus-3/vector-calculus/stokes-and-divergence-theorems) | [Stokes' theorem](/theorems/stokes-theorem), [Divergence theorem](/theorems/divergence-theorem) |

## How students reach MA 26100

| Path | Courses | Credit hours |
| --- | --- | --- |
| With high school calculus | MA 16500, MA 16600, MA 26100 | 4 + 4 + 4 |
| Without high school calculus | MA 16100, MA 16200, MA 26100 | 5 + 5 + 4 |

Both paths meet in MA 26100. See the [MA 16600 guide](/courses/purdue-ma-16600) for the prerequisite material and the [MA 16500 guide](/courses/purdue-ma-16500) 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

$$2(x - 1) - (y - 0) + 3(z - 2) = 0 \quad\Longrightarrow\quad 2x - y + 3z = 8$$

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

$$\frac{dz}{dt} = 2xy \cdot 2t + x^2 \cdot 3 = 2(t^2)(3t)(2t) + 3t^4 = 15t^4$$

which matches differentiating $z = 3t^5$ directly.

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

$$\oint_C -y\,dx + x\,dy = \iint_D (1 - (-1))\,dA = 2 \cdot \pi = 2\pi$$

## How to do well in Purdue MA 26100

- **Picture the geometry.** Sketch surfaces and regions before setting up integrals, and practice [switching the order](/learn/calculus-3/multiple-integrals/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](/theorems/greens-theorem) first, then [Stokes' theorem](/theorems/stokes-theorem) and the [Divergence theorem](/theorems/divergence-theorem).
- **Keep the [formula sheet](/formulas) close** for coordinate conversions, and take timed [practice exams](/practice).
- **See the big picture** in [Calculus 1 vs 2 vs 3](/blog/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.

## Frequently asked questions

### What is MA 26100 at Purdue?

MA 26100, Multivariate Calculus, is Purdue's Calculus 3 course. It covers planes, lines and curves in three dimensions, differential calculus of several variables, multiple integrals and an introduction to vector calculus.

### What do I need to take MA 26100?

A Purdue course outline lists a C- or better in MA 16200 or MA 16600 among the accepted prerequisites, along with several honors and transfer equivalents.

### Is MA 26100 hard?

The new difficulty is working in three dimensions: picturing surfaces and setting up the right bounds. The integration itself mostly reuses Calculus 2 skills.

### What vector calculus is in MA 26100?

A Purdue course outline lists vector fields, line integrals, the Fundamental Theorem for line integrals, Green's theorem, curl and divergence, surface integrals, Stokes' theorem and the Divergence Theorem.

### How should I prepare for MA 26100?

Review vectors and the dot and cross products from MA 16600, and refresh integration by substitution and parts. Our Calculus 3 path starts with the same vector topics.