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4434Mathematical Visualization Toolkit
http://www.merlot.org/merlot/viewMaterial.htm?id=89767
This site consists of a collection of plotting and solving applets featuring a uniform user interface. This site was selected as the 2005 MERLOT Classics Award winner for the Mathematics discipline due to its value and effectiveness as a set of teaching/learning tools. Visualizing mathematical concepts, especially in three-dimensional space, can be quite difficult for students. These tools and applications enable students to see the concepts in action and to come a deeper understanding of the underlying mathematics. In addition, the collaboration between the faculty, students and Sun Microsystems staff who together designed and constructed these tools was quite unusual and impressive. The collaboration itself is an inspiring model.Numerical integration simulation
http://www.merlot.org/merlot/viewMaterial.htm?id=75032
This is a Java-enhanced tutorial that allows students to learn about the rectangular, midpoint, and trapezoidal methods of numerical integration.Visual Differential Equation Solver
http://www.merlot.org/merlot/viewMaterial.htm?id=75573
Solves and graphically displays the solutions to ordinary differential equations. The user can select from an extensive list of standard "Left Hand" (homogeneous) and "Right Hand" (drive) "Sides" or graphically input a drive function. The user also graphically selects a fixed point of the solution. The solution is updated and displayed in real time as all changes are made.Methods for Numerical Integration
http://www.merlot.org/merlot/viewMaterial.htm?id=89893
This applet allows a person to test several numerical integration approximation methods by having the user fill out theleft and right endpoint fields, type in the formula, select the method, and pressing the calculate button. For example trytyping in -1 for the left endpoint, 1 for the right endpoint, and y=x^2 for the formula then press calculate. For each method selected, the estimated integral for that method will appear in the text area at the bottom. Certainfunctions will also appear on the graph on the left. The java graph class is still experimental and does not use equalstretch principles. y = x2 from -1 to 1 will appear the same as y = x2 from -100 to 100.Crank-Nicolson Unsteady State Heat Conduction
http://www.merlot.org/merlot/viewMaterial.htm?id=76093
This Excel application computes and dynamically presents the one-dimensional temperature profiles in an isotropic solid. All computations are performed in Visual BASIC macros. The boundary conditions are convection at the surface and zero flux at the center. The user may select rectilinear, cylindrical, or spherical coordinates. All heat transfer parameters are entered by the user including time step size. The results are graphed at a frequencty set by the user. Tabular results are presented for intermediate time steps elected by the user.DESSolver: Ordinary Differential Equation System Solver
http://www.merlot.org/merlot/viewMaterial.htm?id=85814
This site provides a Java applet that graphs approximate solutions to ODE's using various methods: Runge-Kutta, Euler, Heun, and Dormand Prince. The applet also gives numerical results in tabular form for its solutions.InstaCalc
http://www.merlot.org/merlot/viewMaterial.htm?id=907572
InstaCalc is a customizable calculator designed with the user in mind. Users can specify operations and relationships between entry and output cells and format their own custom designs such as unit converters, loan interest calculators, etc.The platform allows users to save each custom calculator and to copy and embed the code elsewhere so that the calculator can appear on the user's own website. Methods for Estimating Roots
http://www.merlot.org/merlot/viewMaterial.htm?id=89894
This applet allows a person to test several root approximating methods by simply filling in the starting endpoint A, the endingendpoint B, the formula, selecting the method, and pressing the calculate button. For example try typing in 0 for A, 1 for B, andy=x^2-2 for the formula. Press calculate. For each repetition of the method a new line wil be generated in the large text area at the bottom. For equations, which make themethods run many times, you may need to scroll down to the bottom of this text area to view the final output.