Using locus and Geometer's Sketchpad, this video demonstrates how ellipses and hyperbolas are related. Music is by Jan Hammer, from the Miami Vice soundtrack.

Everything you wnated to know about hyperbolas: how to graph them, find vertices, foci, and equations of asymptotes.

How to find the vertex, focus, and directrix of a parabola, given an equation; how to find an equation of a parabola, given a focus and directrix.

An explanation of how to solve exponential and logarithmic equations.

An introduction to logarithmic functions, basic properties of logarithms, and how to graph them.

An explanation of some properties of logarithms, including the change-of-base formula, and the product, quotient, and power properties.

An explanation of the law of cosines and Heron's area formula, with a few examples worked out.

Several examples of verifying trigonometric identities are worked out, along with an explanation of some basic strategies fro verifying identities.

Continuity of functions is defined, one-sided limits are illustrated, and the Intermediate Value Theorem is explained.

How to locate vertical asymptotes of rational functions, as well as evaluate one-sided limits.

An explanation of the basic rules for differentiation: constants, Power Rule, sine and cosine

How to plot a rough sketch of rational functions.

Everything you wanted to know about complex numbers: how to add, subtract, multiply and divide them.

How to graph parabolas from quadratic functions, and how to find the equation of a quadratic function given the vertex and a point of the parabola.

An explanation of mathematical modeling, including linear regression, direct variation, inverse variation, and joint variation.

An explanation of rigid and non-rigid trnasformations of functions, including shifting, reflecting, and scale changes.

An explanation of what inverse functions are, how to graph them, and how to find the inverse of a given function.

How to use calculus to find the maximum or minimum of something described by a function.

A demonstration of some of the tools we can use to graph functions, including the first and second derivatives.

How to evaluate limits of functions as x approaches infinity, and how they help identify horizontal asymptotes.

An explanation of how the second derivative of a function helps determine the concavity of the function, and locates points of inflection. Also, the second derivative can test for whether the function's critical points are relative maximums or minimums.

How to use the first derivative of a function to find the intervals of where it is increasing and decreasing. From that information, we can determine relative minimums and maximums.

An explanation of what Rolle's Theorem and the Mean Value Theorem are, with some examples of how they can be applied.

An explanation of how to determine critical points, and how to locate the extreme values of a function on a closed interval.

An explanation of how to apply the product and quotient rules of differentiation.

This is an explanation of the limit definition of the derivative, and how it calculates the slope of a line tangent to the graph of a function. An example is also worked out the illustrate the concept.

How to graph parametric equations, eliminate the parameter, and convert a rectangular equation to a set of parametric ones.

An explanation of polar equations of conics. We learn how to sketch a conic given its polar equation, and how to find the polar equation given certain parameters of a conic.

An exploration of some special polar graphs: "rose" curves, cardioids & limaçons, and lemniscates.

An introduction to graphing polar equations by hand and with a graphing calculator.

A screencast explaining how to use Sketchpad and the concept of locus to create parabolas, ellipses, and hyperbolas.

An introduction to ellipses and their components: how to graph them, and how to find their equations.

A brief explanation of five different types of exponential models, with several examples of growth and decay problems.

An explanation of how sine and cosine curves are generated, using Geometer's Sketchpad.

Derivation and application of the Law of Sines, with an example of the ambiguous case thrown in for good measure.

How to use some fundamental trig identities (reciprocal, quotient, pythagorean, & cofunction) to simplify trig expressions.

An explanation of how to graph functions involving cosecant and secant.

An introduction to graphing the tangent and cotangent functions.

An introduction to working with radians and degrees, including linear and angular speed.

Finding limits of functions numerically and graphically.

How to use the Fundamental Thm of Algebra to factor higher-degree polynomials.

Lecture on how to perform polynomial division and synthetic division.

How to graph polynomials of degree 3 or more.

A brief lecture on the basic principles of probability.

A brief lecture explaining what permutations and combinations are.