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.
University of Pittsburgh Updated 3 min read
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
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On this page
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 | Dot and cross product |
| Dot and cross product | Cross product | Projections and work |
| Lines, planes and surfaces | Planes in space | Lines in space |
| Curves in space | Curves and motion | Parametric motion |
| Partial derivatives | Partial derivatives | Partial derivatives |
| Gradient and tangent planes | Gradient and directional derivatives | Gradient guide |
| Max and min, Lagrange multipliers | Lagrange multipliers | Lagrange multipliers |
| Double integrals | General regions | Double integrals |
| Triple integrals | Triple integrals | Cylindrical and spherical |
| Line integrals and Green's theorem | Line integrals of vector fields | Green's theorem |
| Stokes' theorem | Stokes and divergence theorems | Stokes' theorem |
| First order differential equations | Separable equations | Differential equations problems |
MATH 0240 in the Pitt sequence
| Course | Credits | Prerequisite |
|---|---|---|
| MATH 0220 Analytic Geometry and Calculus 1 | 4 | C in MATH 0032 or 0200, or placement 76+ |
| 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:
2. A triple integral. The volume of the unit cube:
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.
- Review separable equations before the differential equations unit.
- Use timed practice exams and partial derivatives problems 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.
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Vectors and their length
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