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4434Introduction to Calculus Applets
http://www.merlot.org/merlot/viewMaterial.htm?id=343859
This site consists of several dozen applets, each pertaining to a different aspect of single variable Calculus. Topics covered range from continuity and limits to differential equations and infinite series. Each applet is on a separate page that also includes detailed explanations of the concept under review along with suggestions for student experimentation with the applet. Each applet can be opened in a resizable window for better viewing as a classroom demonstration.Population Modeling Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=314085
In this applet, the user applies Euler's Method to modeling population growth using the Malthus exponential model and the Verhulst constrained growth model. After finding the Euler solution, the user can check the solution with the Adaptive Euler Approximation or with a slope field. Also, the user can enter an exact solution obtained from separating variables (or whatever) and again check the Euler solution graphically.Functions Defined by Series
http://www.merlot.org/merlot/viewMaterial.htm?id=249164
This applet is a sub-site of the Math Applets for Calculus at SLU site. This applet is designed for the visual exploration of functions defined as a sum over k of terms in x. The user can also enter and plot another function: for example, the limit function of the series when it can be expressed in closed form.Escher and the Droste Effect
http://www.merlot.org/merlot/viewMaterial.htm?id=83200
The goal of this site is to visualize the mathematical structure behind M.C. Escher's picture called "Print Gallery" (1956). The visualization itself is largely non-mathematical and is accomplished through many still images and animations. The actual mathematics, involving conformal mappings of the complex plane, is contained in a pdf copy of the original AMS publication. The Droste Effect refers to any image that contains itself on a smaller scale.Sequences and Series Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=249162
This applet is a sub-site of the Math Applets for Calculus at SLU site. This applet provides a graphical interface through which the user can visualize and explore five sequences and their corresponding series. The user has control over a number of parameters including the number of terms, whether to plot terms, sums or ratios, and whether to plot points or lines.Least Squares Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=314427
Quoted from the site: This applet explores fitting a polynomial p(x) of degree n to a given set of data points. It computes the best least squares approximation to the data, "best" in the sense that SUM (p(xi) - yi)^2 is minimized. The applet provides controls for choosing the degree n, setting the precision of all displayed numbers, selecting and deselecting data points, and editing the data list. It also allows for entry of your own custom polynomial and computing its least squares error.Principles of Calculus Modeling: An Interactive Approach
http://www.merlot.org/merlot/viewMaterial.htm?id=297526
Quoted from the site: This Web site contains a page for each section of the book Principles of Calculus Modeling, an Interactive Approach. A section page includes a summary of the section, an on-screen applet demonstrating the key point of the section, and what you should know after studying the material of the section. It also includes links to * additional in-depth applets, * worked examples, * videos of problems being worked out by students and teachers, * a quiz (with answers) that you can take to test your knowledge, * a link to a PDF document with of all the exercises of the section, * a link to these same exercises in interactive form with answer feedback, and * hypertext links to other supplementary materials on the Web that you might find useful, such as sample exams.Basic Ecological Models
http://www.merlot.org/merlot/viewMaterial.htm?id=223092
This is a subsite associated with the parent site called IDEA (Internet Differential Equation Activities). The activity on this page is an introduction to exponential and logistic growth models applied to various ecological systems. Nine problems explore such concepts as asymptotic behaviour, carrying capacity, harvesting, equilibria, and stability. Java applet graphing utilities are conveniently placed throughout to provide visualization of solutions.Determining Continuity Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=314072
In this applet, the user selects or inputs a function and chooses a point x = a at which to check continuity. The applet will calculate several dozen values of f(x) near x = a. From this data, which is presented both in a table and in a graph, the user can make a conjecture regarding continuity at x = a. Limits at infinity are also considered.Taylor Polynomial Approximation Applet
http://www.merlot.org/merlot/viewMaterial.htm?id=249125
This applet is a sub-site of the Math Applets for Calculus at SLU site. This applet provides a graphical interface through which the user can input the function f(x), the point about which to expand, and the degree of the Taylor polynomial approximation. The applet graphs f(x), the Taylor polynomial, and the error function.