## Introduction Calculus is a beautiful mathematical subject with striking applications in science and engineering. In Calculus I, you learned about the main objects in calculus: the derivative and the integral. In this class, we will study their use in mathematics and applications. Broadly speaking, you will learn to integrate complicated functions, use integration techniques to solve differential equations stemming from physical systems, use sequences and series to compute or approximate functions, and study geometric objects using tools from calculus.

The material covered will be drawn from the following: Techniques of integration, including integration by parts, simple trig substitutions, partial fractions. Basic numerical integration; improper integrals; arc length; area of surface of revolution. Separable differential equations, Euler's method, exponential growth and decay. Parametric curves and polar coordinates. Review of conic sections. Sequences and series, comparison and ratio tests, Taylor series and polynomials. Vectors in three dimensions, dot product, cross product, lines, planes, cylinders, quadric surfaces; cylindrical and spherical coordinates.