UGA MATH 2270 Calculus III: Syllabus, Topics and Practice

UGA MATH 2270 (Calculus III for Science and Engineering) is the third course in the University of Georgia's science and engineering calculus sequence. It is a 4-credit-hour course offered every fall, spring and summer. This guide maps the official topic list to lessons you can practice with instant feedback.

What UGA MATH 2270 covers

The UGA Department of Mathematics describes MATH 2270 as the calculus of functions of two and three variables: parametric curves and applications to planetary motion. Derivatives, the gradient, Lagrange multipliers. Multiple integration, area, volume, and physical applications, polar, cylindrical, and spherical coordinates. Line and surface integrals, Green's, Stokes's, and Divergence theorems, with applications to physics.

That is a full Calculus 3 course. Because UGA introduces vectors, dot and cross products, and lines and planes in MATH 2260, MATH 2270 can move quickly into curves, partial derivatives, multiple integrals and vector calculus. The department page does not list a schedule or textbook; it links a syllabi lookup.

MATH 2270 topic map

MATH 2270 in the UGA sequence

Example problems at the MATH 2270 level

1. Velocity and speed. For \mathbf{r}(t) = \langle \cos t, \sin t, t \rangle:

2. A spherical integral. The volume of a ball of radius R:

3. The Divergence Theorem. For \mathbf{F} = \langle x, y, z \rangle over the unit ball, \nabla\cdot\mathbf{F} = 3, so the outward flux is 3 \cdot \frac{4}{3}\pi = 4\pi.

How to do well in MATH 2270

• Review the MATH 2260 vectors unit first. Dot and cross products drive everything from tangent planes to flux.
• Sketch regions and solids before setting up any multiple integral.
• Memorize the volume elements: r\,dr\,d\theta in polar and cylindrical, \rho^2\sin\phi\,d\rho\,d\phi\,d\theta in spherical.
• Compare the big theorems side by side using the vector calculus summary.
• Practice with Lagrange multipliers problems and timed practice exams.

Tip: if a surface is closed and the divergence is simple, the Divergence Theorem usually turns a hard flux integral into an easy volume integral.