Category: College Algebra

Calculus and Precalculus Review Sites

Here is a little collection of Calculus and Precalculus review materials. This calculus review website (at San Jose State University) is a nice interactive site that could be used on a campus website to help students review for Calc II or III. Information on creating a quiz for the web (like this one) is published on Valdez’ website here. She has a second “review” resource called “Preparing for the Mathematics Placement Exam” that can be found here. It is essentially all the math you need to have learned BEFORE you take calculus. I have also found the Visual Calculus webpages to be a great place for students to review, although some of the links no longer function and the material does not seem to be updated anymore. These contain some nice flash tutorials.     Purplemath (put up by Elizabeth Stapel) is a good site for reviewing precalculus skills as well, although I could really do without the ads advertising “cheat” software… which almost made me leave it off of our department website.   Especially because of the lack of advertising, you might prefer Paul’s Online Math Notes, which contains a plethora of information on topics ranging from algebra through Differential Equations. I do wish he would consider calling the “cheat sheets” by another name, perhaps “formula sheets” or “reference pages” would be a more appropriate name. Our department...

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Radioactive Decay

This Radioactive Decay Java applet can be found in the National Curve Bank. It was written by Cindy So (Cal State LA) and includes all the data you’d ever need to do realistic radioactive decay problems. You can use the Java applet to compare graphs of elements with different decay rates, and calculate the age of an item based on the original and remaining amounts, among other things. There is also a nice historical plot of the Carbon-14 decay rate with various items and their Carbon-14 dated age. Although radioactie decay problems are often thought of as precalculus level problems, remember that calculus students can also do these problems by looking at the differential equation that describes the rate of decay (also described on this site). Possibly Related Posts: Contemporary Algebra Collection (new resources 2/4/2019) Add Graphs In The World to Courses Bringing the Real World to Your Math Class Every Day Taking the Algebra Out of College Algebra Group Exploration in...

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Famous Curves Index

I found this nice website while looking around the website of a community college in Maine. The Famous Curves Index (published by a school of mathematics in Scotland) has 63 famous curves complete with equations, graphs (like this nice one of Fermat’s Spiral below), a short history of the curve, and a link to interactive Java code for manipulating the curve. This one is the interactive Java code for a Hypocycloid (given by a parametric equation)… very nice! What a great resource for Precalculus and Calculus classes. I will have to pull up some of these curves next week when we talk about implicit differentiation. If you’re teaching parametric equations or polar equations, this site would be great! I didn’t have any trouble getting the Java applets to work. Kudos to the School of Mathematics and Statistics, University of St. Andrews, Scotland for a great collection of curves! Possibly Related Posts: Contemporary Algebra Collection (new resources 2/4/2019) Add Graphs In The World to Courses Bringing the Real World to Your Math Class Every Day Taking the Algebra Out of College Algebra Group Exploration in...

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Progress in Technology is EXPONENTIAL

Today I am forwarding you on to Ray Kurzweil’s Ted Talk “How technology’s accelerating power will transform us” This whole talk is about exponential trends. There are several beautiful log-plots of modern examples of exponential growth and decay. DNA Sequencing, World-wide-web, size of computers, Moore’s Law, evolution of technology, etc. He also talks about their research creating mathematical models to predict trends in technology. There is also an interesting segment in here on proposed nanobot red blood cells (tiny spheres that act as red blood cells, only more efficiently)… fascinating. Kurzweil predicts we will have succeded at reverse-engineering the human brain by the year 2020. By 2029… we won’t even see computers anymore. Computers will be integrated into our brains, clothing, and bodies. The merging of our brains with technology will provide us with the intelligence to evolve to the ability to understand our own intelligence. Just for the record, I will still be YEARS away from retirement in 2029… so while this might not concern you… I have to consider it a real possibility during my teaching career. How will we train a brain that integrates nanobots? Will that be considered “cheating” or no different than the use of a graphing calculator to assist in drawing a function? Yikes! I became curious about Ray Kurzweil after watching his talk, and spent some time poking around his websites

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Line Rider, in its infancy, had only one tool, the pen. With this tool, you drew your masterpiece curve (or piecewise curves), on which, the little hatted dude rides his sled. There were rules about the curves, when drawn left to right, the were riding curves, when drawn right to left, decoration… or something like that. However, the new version of LineRider has multicolored pens, an eraser tool (woo hoo) and now with the addition of the magical Jing program… I can easily record and share my masterpiece with you. If you watch my masterpiece, keep in mind that I have just nicely demonstrated two types of discontinuities in my work… removable discontinuities (the little dude just glides over the hole) and jump discontinuities (the little dude leaps from one part of the curve to another). LineRider can be an interesting and fun study in slopes for algebra students, asymptotes for pre-calculus students, and limits for calculus students. However, the true works of art are the ones created and set to music like these classic LineRiders all available on YouTube: (turn on your sound) Jagged Peak Adventure Urban Run Electronic Adventures LineRider SuperMario (okay… that one is really clever!) These are good for a 5-minute break in class… you know… for those students that refuse to get out of their seats and stretch… they might as well be entertained!...

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