# Pitt MATH 0240 Calculus 3: Syllabus, Topics and Practice

> A study guide for Pitt MATH 0240 Analytic Geometry and Calculus 3: vectors, surfaces, partial derivatives, multiple integrals and Stokes' theorem.

Source: https://practicecalculus.com/courses/university-of-pittsburgh-math-0240
Updated: 2026-11-08

## At a glance

- **Course code:** MATH 0240
- **Credits:** 4
- **Prerequisites:** C or better in MATH 0230
- **Covers:** Vectors and surfaces in space, calculus of functions of several variables including partial derivatives and multiple integrals, Stokes' theorem, first order differential equations
- **Honors version:** MATH 0245 Honors Multivariable Calculus
- **Practice here:** [Calculus 3](/learn/calculus-3)

## Key takeaways

- MATH 0240 is the 4-credit third course in the University of Pittsburgh's basic calculus sequence.
- It covers vectors and surfaces in space, partial derivatives, multiple integrals, Stokes' theorem and first order differential equations.
- The prerequisite is a C or better in MATH 0230.
- MATH 0245 Honors Multivariable Calculus is the enriched version.

**Pitt MATH 0240** (Analytic Geometry and Calculus 3) is the last of the three basic calculus courses at the University of Pittsburgh, after MATH 0220 and MATH 0230. It carries 4 credits and requires a C or better in MATH 0230. This guide maps each topic from the department's description to lessons you can practice with instant feedback.

## What Pitt MATH 0240 covers

The Pitt mathematics department describes MATH 0240 as the third of a sequence of three basic calculus courses. It covers vectors and surfaces in space and the calculus of functions of several variables, including partial derivatives and multiple integrals, Stokes theorem, and first order differential equations.

That is a full **Calculus 3** course with a short unit on differential equations added. It is the natural next step after MATH 0230 for engineering, physics and mathematics students, and the vector skills from the first weeks are used in every later topic. The department page links a syllabus example for textbook, grading and schedule details, which can change from term to term.

## MATH 0240 topic map

| MATH 0240 topic | Practice | Read |
| --- | --- | --- |
| Vectors | [Vectors and length](/learn/calculus-3/vectors-and-space/vectors-and-length) | [Dot and cross product](/blog/vectors-dot-and-cross-product) |
| Dot and cross product | [Cross product](/learn/calculus-3/vectors-and-space/cross-product) | [Projections and work](/learn/calculus-3/vectors-and-space/projections-and-work) |
| Lines, planes and surfaces | [Planes in space](/learn/calculus-3/vectors-and-space/planes-in-space) | [Lines in space](/learn/calculus-3/vectors-and-space/lines-in-space) |
| Curves in space | [Curves and motion](/learn/calculus-3/vectors-and-space/curves-and-motion) | [Parametric motion](/learn/calculus-2/power-series-parametric-polar/parametric-motion) |
| Partial derivatives | [Partial derivatives](/learn/calculus-3/partial-derivatives/partial-derivatives) | [Partial derivatives](/blog/partial-derivatives) |
| Gradient and tangent planes | [Gradient and directional derivatives](/learn/calculus-3/partial-derivatives/gradient-and-directional-derivatives) | [Gradient guide](/blog/gradient-and-directional-derivatives) |
| Max and min, Lagrange multipliers | [Lagrange multipliers](/learn/calculus-3/partial-derivatives/lagrange-multipliers) | [Lagrange multipliers](/blog/lagrange-multipliers) |
| Double integrals | [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) | [Cylindrical and spherical](/learn/calculus-3/multiple-integrals/cylindrical-spherical) |
| Line integrals and Green's theorem | [Line integrals of vector fields](/learn/calculus-3/vector-calculus/line-integrals-of-vector-fields) | [Green's theorem](/theorems/greens-theorem) |
| Stokes' theorem | [Stokes and divergence theorems](/learn/calculus-3/vector-calculus/stokes-and-divergence-theorems) | [Stokes' theorem](/theorems/stokes-theorem) |
| First order differential equations | [Separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations) | [Differential equations problems](/practice-problems/differential-equations) |

## MATH 0240 in the Pitt sequence

| Course | Credits | Prerequisite |
| --- | --- | --- |
| [MATH 0220](/courses/university-of-pittsburgh-math-0220) Analytic Geometry and Calculus 1 | 4 | C in MATH 0032 or 0200, or placement 76+ |
| [MATH 0230](/courses/university-of-pittsburgh-math-0230) Analytic Geometry and Calculus 2 | 4 | MATH 0220 (or 0120 + 0205), C or better |
| MATH 0240 Analytic Geometry and Calculus 3 | 4 | C or better in MATH 0230 |

## Example problems at the MATH 0240 level

**1. A directional derivative.** For $f(x, y) = x^2 + y^2$ at $(1, 2)$ in the direction $\mathbf{u} = \langle \frac{3}{5}, \frac{4}{5} \rangle$:

$$D_{\mathbf{u}} f = \nabla f \cdot \mathbf{u} = \langle 2, 4 \rangle \cdot \left\langle \tfrac{3}{5}, \tfrac{4}{5} \right\rangle = \frac{22}{5}$$

**2. A triple integral.** The volume of the unit cube:

$$\int_0^1 \int_0^1 \int_0^1 dz\,dy\,dx = 1$$

**3. A first order equation.** If $y' = xy$, then $\frac{dy}{y} = x\,dx$, so $y = Ce^{x^2/2}$.

## How to do well in MATH 0240

- **Sketch every surface and region.** It is the single most useful habit in Calculus 3.
- **Keep your Calculus 2 integration skills sharp,** since every multiple integral ends in single-variable integrals.
- **Practice the big theorems side by side.** Learn what each one needs (closed curve, surface with boundary, closed surface) using the [vector calculus practice](/learn/calculus-3/vector-calculus/vector-calculus-practice).
- **Review [separable equations](/learn/calculus-2/improper-integrals-and-applications/separable-equations)** before the differential equations unit.
- **Use timed [practice exams](/practice)** and [partial derivatives problems](/practice-problems/partial-derivatives) before tests.

> **Tip:** for a triple integral, choose the coordinates that match the shape. A cylinder is easiest in cylindrical coordinates and a ball in spherical coordinates.

## Frequently asked questions

### What is MATH 0240 at Pitt?

MATH 0240 Analytic Geometry and Calculus 3 is the third of three basic calculus courses at Pitt. The department says it covers vectors and surfaces in space and the calculus of functions of several variables, including partial derivatives and multiple integrals, Stokes theorem, and first order differential equations.

### What is the prerequisite for MATH 0240?

A grade of C or better in MATH 0230.

### Does MATH 0240 include differential equations?

Yes, the department description lists first order differential equations. For a full course on the subject, MATH 0250 Matrix Theory and Differential Equations also needs a C or better in MATH 0230.

### Is there an honors version of MATH 0240?

Yes. MATH 0245 Honors Multivariable Calculus covers the same topics in greater depth with more challenging problems. It requires consent of the Honors College.

### How hard is MATH 0240?

Most students say the hardest part is visualizing surfaces and regions in three dimensions. Once you can sketch the region, setting up and computing the integrals is mostly Calculus 1 and 2 skills.