Math 104 Online

Welcome: About This Course

This course is built in Ximera.

1Applications 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.

1.1Volume By General Cross Sections

We use cross-sectional area to compute volume.

1.3The Disk and Washer Methods

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

1.5The Shell Method

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

1.7Synthesis: Choose Your Method

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

1.9Arc Length

We practice setting up and executing arc length calculations.

1.11Surface Area

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

1.13Centers of Mass and Centroids

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

2Integration Techniques

We begin a study of techniques for computing integrals.

2.1Substitution and Tables

We review substitution and the use of integral tables.

2.3Integration by Parts

We study the integration technique of integration by parts.

2.5Trigonometric Integrals

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

2.7Trigonometric Substitions

We practice executing trigonometric substitutions.

2.9Partial Fractions

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

3Further Topics in Integration

We study additional topics relating to applications of integration.

3.1Numerical Integration

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

3.3Orders of Growth

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

3.5Improper Integrals

We study the concept of improper integrals.

3.7Probability

We study probability and its connections to integration.

4Sequences and Series

We begin a study of sequences and series.

4.1Sequences

We study the mathematical concept of a sequence.

4.3Series

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

4.5Series Comparison Tests

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

4.7The Ratio and Root Tests

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

4.9The Integral Test

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

4.11Alternating Series

We study the notion of alternating series and related concepts.

5Power Series

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

5.1Power Series

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

5.3Taylor Series

We introduce the notion of a Taylor Series.

5.5Taylor Series Applications

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

6Ordinary Differential Equations

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

6.1ODEs: Foundations

We study the fundamental concepts and properties associated with ODEs.

6.3Separable and Linear ODEs

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

6.5Applications of ODEs

We study some sample applications of ODEs.