Welcome: About This Course

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.

Synthesis: Choose Your 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.


We study probability and its connections to integration.

Sequences and Series

We begin a study of sequences and series.


We study the mathematical concept of a sequence.


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.

You can download a Certificate as a record of your successes.