We review differentiation and integration.

We introduce the procedure of “Slice, Approximate, Integrate” and use it study the area of a region between two curves using the definite integral.

We can also use the procedure of “Slice, Approximate, Integrate” to set up integrals to compute volumes.

We can use the procedure of “Slice, Approximate, Integrate” to find the length of curves.

We compute surface area of a frustrum then use the method of “Slice, Approximate, Integrate” to find areas of surface areas of revolution.

We apply the procedure of “Slice, Approximate, Integrate” to model physical situations.

We learn a new technique, called integration by parts, to help find antiderivatives of certain types of products by reexamining the product rule for differentiation.

We can use substitution and trigonometric identities to find antiderivatives of certain types of trigonometric functions.

We integrate by substitution with the appropriate trigonometric function.

We discuss an approach that allows us to integrate rational functions.

We can use limits to integrate functions on unbounded domains or functions with unbounded range.

A sequence is an ordered list of numbers.

A sequence can be thought of as a function from the integers to the real numbers. There are two ways to establish whether a sequence has a limit.

A series is summation of a sequence.

Infinite sums can be studied using improper integrals.

If an infinite sum converges, then its terms must tend to zero.

Some infinite series can be compared to geometric series.

Some infinite series can be compared to geometric series.

We compare infinite series to each other using inequalities.

We compare infinite series to each other using limits.

Alternating series have nice properties.

We can approximate smooth functions with polynomials.

Infinite series can represent functions.

We study Taylor and Maclaurin series.

Taylor series are a computational tool.

Power series interact nicely with other calculus concepts.

Differential equations show you relationships between rates of functions.

We describe numerical and graphical methods for understanding differential equations.

Separable differential equations are those in which the dependent and independent variables can be separated on opposite sides of the equation.

We discuss the basics of parametric curves.

We discuss derivatives and integrals of parametric curves.

Polar coordinates are a special type of parametric curves.

We see a collection of polar curves.