Converting Polar & X-Y Equations
This video covers the tricks you'll need to convert Cartesian equations to Polar, and vice versa.
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Converting Points Between Polar & Cartesian
This is basically a review of a particular type of unit circle problem, but it's a good first step in learning to convert equations between x-y coordinates and polar. Don't forget to check your quadrant!
Plotting Polar Functions by Plug-and-Chug
Plotting polar graphs is obviously a lot easier when you have everything memorized and practiced. But what if you don't have them quite memorized, or the one on the test is confusing? Start plugging in angles, getting points, and connecting the dots!
Polar Coordinates On Your Calculator
Students often have trouble with graphing on their calculators, and it's even harder with polar coordinates. So in this short video I show you a few pitfalls to avoid, especially getting that window size set right so that things that are round look round.
Plotting Points in Polar Coordinates
You may think you already know how to plot polar coordinates, but this video covers the subtleties which can mess you up later, such as what to do with negative r's, and the wacky fact that lots of different-looking coordinates can actually all refer to the same point.
This chapter covers everything from graphing polar coordinates and functions to converting equations between polar and Cartesian x-y coordinates. Also, how to do these on your calculator!
Area of Sectors
These problems tend to be a lot easier than arc length because, well, sectors are boring. There aren't a lot of fancy word problems to play with. That said, there are a few tricks teachers can pull. Also, if you've got a standardized test coming up (SAT, GRE, etc.), I'll show you how to do these problems in a simple, formula-free way.
Arc Length Word Problems
Word problems are where arc length usually gets tricky, and depending on your teacher, these can get really tough! And often teachers make things harder by asking questions about bike gears and cars where you have to find the velocity of the bike based on how fast the wheels or cranks are turning. Not easy, but this video gets you through the most common types of questions.
Basic Arc Length Problems
The formula is so simple that there's only a few tricks a teacher can pull on an arc length without making it a word problem. Also, if you've got a standardized test coming up (SAT, GRE, etc.), you probably won't remember the formula on test day, so I'll also show you how to do these problems in a simple, formula-free way.
This chapter covers the basics of arc length and sector area, as well as difficult word problems about bike gears, vehicle speed, planets, and velocity of rotating objects.
Even & Odd Functions In A Nutshell
This video covers the main stuff you'll need to know about even and odd functions: what they are, how to identify them based on the symmetry in a graph (y-axis symmetry and origin symmetry), and the quick ways to spot them based on their equations. The next video will be about how to "prove" or "verify" that they're even or odd "algebraically".
Using Definition of Even & Odd Functions
The more mathy (thus harder) type of even and odd function problem is when they ask you to "verify" or "prove" or "show algebraically" that a function is even, odd, or neither. This video gets you through that and shows you the typical traps that a teacher will set for you in this chapter.
Usually in math, the names don't make any sense. But this is an exception: "even" and "odd" refer to whether the exponents on the x's are even or odd!
Interval of Convergence
Extending on the previous video, these interval of convergence problems start the same way as radius of convergence problems, except that you then must test the endpoints to see if they result in a convergent series.
Power Series Radius of Convergence
This video introduces the concept of radius of convergence, and takes you through the step-by-step process using the Ratio Test that you'll use for these problems. If you don't remember the ratio test, review this chapter.
This chapter covers radius of convergence and intervals of convergence for power series, which are just the generic name for infinite series like Taylor and Maclaurin.
Approximating Functions With Taylor & Maclaurin Series
Finally, it's time to start approximating some stuff! Why approximate anything when I can just type it into my calculator, you ask? Well, mister, put yourself in the shoes of someone in the 1700's, before they had calculators and slide rules (look it up), and you'd be thanking your lucky stars that you have a way to calculate ln(1.1) and e.1. Yeah, not so sassy now are you?
Taylor & Maclaurin Series Examples
In this video we go through some more examples of working out the expansions of a few common functions. Hopefully by the end of this, you'll be getting the hang of these things so we can start calculating stuff with them.
Intro to Taylor & Maclaurin Series
This video introduces these complicated series, and tries to show you that they're really not that bad. Also included are a couple of hot tips to help you memorize the nasty-looking Taylor Series expansion formula, and for those who want to "understand stuff", I spend about a minute explaining how the Taylor & Maclaurin expansions are really just linear approximations with an extra couple terms thrown on.