Dynamic Calculus - Welcome
Calculus Function Grapher
Riemann Sum Applet
Antiderivative Graph Example
Direction Field Applet
Excel Calculus Explorations - Descriptions
Multivariable Calculus Exploration (NSF grant project)
NSF Multivariable Calculus Project Site
Hughes-Hallett Calculus Applets
Updated Anton Calculus Applets
Larson Calculus Applets
Create New Topic
Welcome to my Dynamic Calculus Website!
This part of my site is likely to change frequently in the next year. Presently there are several applets that can be selected from the sidebar to the left.
Calculus Function Grapher: A basic function grapher that allows you to copy and paste graphs into Word. It allows graphs of y = f(x), x = f(y), polar, parametric, and piecewise functions. You can graph up to four separate functions of x at a time (or three ordinary functions with a single piecewise function). It attempts to handle vertical asymptotes correctly (even displaying them if you like) and does pretty well with jump and removeable discontinuities as well (at least for integer values of x). A tangent line can be moved along the graph of any function of x, you can have the function's derivative graph displayed with the function to examine their relationship, and you can also explore the area function that corresponds to the present function of x. Please give me your feedback, if you have comments or suggestions!
Larson Calculus applets: This is a set of 6 applets that I wrote for Larson Calculus while they were still owned by Houghton Mifflin. There were supposed to be a total of 43 applets supporting this text. Now that Cengage has taken over, they decided not to continue with the project. If you find these applets useful, please tell your Cengage book rep that you are using them and that you would enjoy seeing more applets like these made available to support Larson Calculus. (Thanks!)
The page Excel Calculus Explorations - Descriptions lists the resources available through this website, giving some screenshots and some description for each. In order to download most of the materials, I ask that you register as a member of this site. This allows me to get a sense of how many people are interested in these materials and it allows interested people to engage in discussion on the site. No personal information will be shared with anyone else. I may from time to time email members with questions concerning the materials on the site or with announcements about updates or changes.
Once you register as a member and login to this site, another option will appear on the navigation bar to the left. Follow that link to Excel Calculus Explorations - Downloads and you will be able to download my calculus explorations for Excel and several handouts from my recent conference presentations.
Presently many of my other Java applets are housed on my faculty home page, but eventually most or all of them will be moved here.
Why use visual explorations like these in Calculus?
Calculus is the mathematics of change. The definitions of each of the basic concepts of Calculus, the limit, the derivative, and the integral are all dynamic. So, if we really want to understand the basic definitions and concepts of Calculus, we need to see them in motion… to see the change in a dynamic and living way. Seeing a few static diagrams can be helpful (I believe it is still very helpful to start our definitions on the chalk board in many cases), but if the diagrams come to life and we are allowed to manipulate them (and have fun with them!), our understanding of the relationships involved can improve dramatically. From what my students have told me, they find this approach to be interesting, very helpful, and many times even fun! As we explore Calculus using the explorations I am creating, I hope my students may also begin to appreciate some of the intricate and fascinating beauty of the mathematics of Calculus.
In addition to simply watching me interact with the concepts dynamically, I also believe my students benefit greatly when they interact dynamically with these concepts themselves. I have designed these computer explorations to be used in both of these ways, as classroom demonstrations and also as student explorations outside of class. From my experience, in order for most students to make active use of this kind of exploration, it is very helpful to require them to complete guided exploration activities that I call “labs” outside class. I have created a number of these lab activities so far, and I will continue to create them, to help my students to get their hands “dirty” playing with the Calculus concepts visually. One of my major goals for this project is to develop my students’ geometric intuition about the concepts we cover in calculus, helping them to understand these concepts more deeply and make connections between them visually in a way that has been difficult without such software.