This course is built in Ximera.

#### Applications of Integration

We study some important application of integrations: computing volumes of a variety of complicated three-dimensional objects, computing arc length and surface area, and finding centers of mass.

#### Volume By General Cross Sections

We use cross-sectional area to compute volume.

#### The Disk and Washer Methods

We practice setting up calculations related to the disk and washer methods.

#### The Shell Method

We practice setting up setting up volume calculations using the shell method.

We practice choosing a method for computing volume when none is specified.

#### Arc Length

We practice setting up and executing arc length calculations.

#### Surface Area

We practice setting up integrals for the surface area of surfaces of revolution.

#### Centers of Mass and Centroids

We practice setting up calculations for centers of mass and centroids.

#### Integration Techniques

We begin a study of techniques for computing integrals.

#### Substitution and Tables

We review substitution and the use of integral tables.

#### Integration by Parts

We study the integration technique of integration by parts.

#### Trigonometric Integrals

We learn various techniques for integrating certain combinations of trigonometric functions.

#### Trigonometric Substitions

We practice executing trigonometric substitutions.

#### Partial Fractions

We study the technique of partial fractions and its application to integration.

#### Further Topics in Integration

We study additional topics relating to applications of integration.

#### Numerical Integration

We study the problem of numerically approximating the value of an integral.

#### Orders of Growth

We study the use of orders of growth to compute limits, in preparation for improper integrals.

#### Improper Integrals

We study the concept of improper integrals.

#### Probability

We study probability and its connections to integration.

#### Sequences and Series

We begin a study of sequences and series.

#### Sequences

We study the mathematical concept of a sequence.

#### Series

We introduce the concept of a series and study some fundamental properties.

#### Series Comparison Tests

We study the direct and limit comparison theorems for infinite series and practice their application.

#### The Ratio and Root Tests

We study the ratio and root tests for infinite series and practice their application.

#### The Integral Test

We study the integral test for infinite series and related concepts.

#### Alternating Series

We study the notion of alternating series and related concepts.

#### Power Series

We undertake a study of an important class of infinite series.

#### Power Series

We introduce the concept of a power series and some related fundamental properties.

#### Taylor Series

We introduce the notion of a Taylor Series.

#### Taylor Series Applications

We study the use of Taylor series for evaluating infinite series and limits.

#### Ordinary Differential Equations

We begin a study of first-order ordinary differential equations.

#### ODEs: Foundations

We study the fundamental concepts and properties associated with ODEs.

#### Separable and Linear ODEs

We learn techniques to solve first-order linear and separable ODEs.

#### Applications of ODEs

We study some sample applications of ODEs.