Education - Mathematics

Planet Explorer 1.2

3D Spaceship Simulator/Trainer for 3D thinking. Planet Explorer is a 3D spaceship simulator and trainer for thinking in 3D. It works in two modes: static and dynamic. In dynamic mode the user circulates one of our nine planets on a Kepler ellipse, each planet having a different stationary position. This app shows 3D geometry in action. The simulator interface allows to change all orbit parameter and displays continuously the present position and velocity of the spaceship. In static mode the program uses two other interfaces: a graphics display and an exercise database including numerous self-study topics and exercises. Both interfaces offer an easy, step-by-step, game-like learning framework, where a user is guided from simple to more complex topics, which incorporate fun, game, and self-discovery features. Planet Explorer automatically displays the number of exercises you have done and tried to do, the number of correct answers, as well as your grade, and enables you to create your own topics, exercises, and images as wanted.

Virtual Basketball 1.3

True-Motion Basketball Match Simulator. Virtual Basketball is a true-motion match simulator designed for learners with an interest in science/math. It models ball movements under varying physical conditions. Virtual are a team's changing gravity and ball friction caused by e.g. wind. Two teams, Red-City Bulls and Blue-City Lakers, are competing against each other, attacking and defending. The defending team uses the Tab and Arrow keys of the keyboard and changes its gravity vector and ball friction with Arrow LEFT ++40 units, Arrow RIGHT --40 units, Arrow UP ++1 unit, Arrow DOWN --1 unit, resulting in a different ball motion. The attacking team uses the mouse to shoot balls by: 1) pressing the left mouse button on the court marking the position of a player, 2) keeping (!) the button down, moving to another position and releasing it giving the ball's speed and direction. As in reality, the motion and result of each shot are computed according to the laws of gravity and friction, and visually displayed on the computer screen. After one team has scored, its gravity vector and ball friction are randomly changed (or manually by the other team) so that it becomes much harder to score again. This is the easy way to play the game. The difficult way is to allow the defending team to change its gravity and friction values all the time. The statistics of both teams, their number of scores and tries as well as the average distances of all shots are automatically recorded and displayed in another window. The goal of this program is to teach a user to understand better 1) how the motion of a ball depends on its position, direction, speed, and friction, 2) how the laws of gravity and friction (the acting forces) effect the movement of a flying object, 3) how motion and forces are interrelated, and 4) how to predict the motion of an object (see the Appendix in the Help file for further information).

CurvFit 5.09

CurvFit (tm) is a curve fitting program for Windows 95/98. Lorentzian, Sine, Exponential and Power series are available models to match your data. A Lorentzian series is highly recommended for real data especially for multiple peaked and/or valleys data. CurvFit is an example of Fortran Calculus programming... ie. minutes to solve, days or years to understand solution and what it implies (e.g. wrong model, sampling rate error, etc.). Helps learn 1) whether math model is good for given data; 2) convergence implies a reasonable solution; 3) how to select new starting initial parameter values. See comments in EX*.? files for ideas on how to converge via solvers.Equation Calculator and Hardcopy Plot prints are now (6/2005) available.

ODEcalc 5.09

ODEcalc for Windows: An Ordinary Differential Equation (ODE) Calculator! State your equation and boundary or initial value conditions and it solves your problem. Plots solution y and derivative ydot versus x. Solves most Boundary Value Problems (BVP) and Initial Value Problems (IVP) for Nth order ODE. ODE may be non-linear, implicit, and any order. Source code included ... it's short! Great teaching tool! Helps students understand difference in BVP and IVP plus their importance in solving practical ODEs. ODE and algebraic system of equations may be solved using the methodology in this demo. Hardcopy prints in Windows is now available. This is a Fortran Calculus demo application.