UGA MATH 2260 Calculus II: Syllabus, Topics and Practice

UGA MATH 2260 (Calculus II for Science and Engineering) is the second 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, with MATH 2250 or MATH 2300H as the prerequisite. This guide maps the official topic list to lessons you can practice.

What UGA MATH 2260 covers

The UGA Department of Mathematics describes MATH 2260 as: volumes, arclength, work, separable differential equations. Techniques of integration. Sequences and series, convergence tests, power series and Taylor series. Vectors in three-dimensional space, dot product, cross product, lines and planes.

So MATH 2260 is a full Calculus 2 course plus a short unit on vectors that many other universities put in Calculus 3. The official description does not mention parametric equations or polar coordinates. A weekly schedule and textbook are set by the department and your instructor; the department page links a syllabi lookup.

MATH 2260 topic map

MATH 2260 in the UGA sequence

How MATH 2260 builds on MATH 2250

MATH 2260 assumes you can differentiate quickly and evaluate definite integrals with the Fundamental Theorem of Calculus. It first uses integrals as a tool for volumes, lengths and work, then adds new techniques for harder integrals, then turns to infinite series, and finally steps into three dimensions with vectors. If your MATH 2250 integrals feel rusty, warm up with antiderivative practice and u-substitution.

Example problems at the MATH 2260 level

1. A volume by disks. Rotating y = \sqrt{x} on [0, 4] about the x-axis:

2. A separable equation. If \frac{dy}{dx} = \frac{x}{y}, then y\,dy = x\,dx and y^2 - x^2 = C.

3. A dot product. \langle 2, -1, 3 \rangle \cdot \langle 1, 4, 2 \rangle = 2 - 4 + 6 = 4.

How to do well in MATH 2260

• Draw every volume and work problem. One labeled slice tells you the integral.
• Practice choosing an integration technique with choosing a strategy.
• Leave plenty of time for series. Work through series practice and convergence tests problems.
• Do not treat the vectors unit as an afterthought. It is the foundation of MATH 2270.
• Use timed practice exams before each test.

Tip: for a power series, find the radius with the ratio test, then check each endpoint separately. The endpoints often behave differently.