**Course** Description: | 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. |

**Course Objectives:** | The student will learn how to solve a variety of applied
problems using the integral, including modeling problems by
differential equations. The student will learn how to test
numerical series for convergence and then apply this to power
series and Taylor series approximations. The student will,
lastly, acquire familiarity with vector algebra and geometry
and apply this to lines and planes in three-dimensional space. |

**Topical Outline:** | 1. Review of the definition of the integral, Fundamental Theorem
of Calculus, area, and integration by substitution.
2. Volumes: cross-sections, cylindrical shells. Arclength and
surface area. Work.
3. Separable differential equations.
4. Methods of integration: integration by parts, trigonometric
substitutions, partial fractions. Improper integrals.
5. Sequences, series, convergence tests. Power series, Taylor
series and applications.
6. Vectors in three dimensions. Dot product, cross product,
lines and planes. |