New uCOMP collection resources

Math Animated

Thu, 04 Mar 2010 21:00:33 EST

This web site contains courseware for single and many-variables calculus designed for introductory undergraduate physics and engineering students. Included are text explanations and solved exercises, supported by animated and interactive graphics. The graphics make the material useful for a broader audience in both the classroom and by individual students. These materials use MathML and SVG. The free Firefox browser can be used to view, these resources without any plugins on Windows, Mac and Linux.

Tethered Mass and Spring Model

Sun, 20 Sep 2009 21:28:17 EST

The Tethered Mass and Spring model shows a mass constrained to move in the x-direction by a horizontal rod and connected to a spring of natural length L = 10. One end of the spring is connected to a movable (draggable) ceiling and the other end is connected to the mass. Users can drag the mass along the rod and users can control the height of the ceiling H by dragging which changes the stretch of the spring. The height H, the spring constant k, and the natural length of the spring L can also be adjusted using the sliders at the bottom of the position vs. time graph. The Tethered Mass and Spring model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double click the ejs_mech_lagrangian_TetheredMassAndSpring.jar file to run the program if Java is installed.

An Integer Programming Model for the Sudoku Problem

Sun, 20 Sep 2009 21:27:35 EST

The "Integer Programming Model for the Sudoku Problem" article in the The Journal of Online Mathematics and Its Applications uses an EJS binary integer linear program to solve this feasibility problem. Further, such an approach is extended to variations on the traditional Sudoku puzzle. In addition, we speculate as to how Sudoku puzzles are created, and provide several theorems for generating many new puzzles from one given original puzzle. EJS models allow for exploration with a variety of the ideas. Readers with Matlab and its Optimization Toolbox can solve Sudoku puzzles directly from an applet. Exercises and challenge problems that use principles from optimization, combinatorics, linear algebra, and computer science are presented for students.

Mountains of Fractals

Sun, 20 Sep 2009 21:27:11 EST

The "Mountauns of Fractals" article in the Math DL develops algorithms to produce coastlines and mountains in two dimensions by adapting mathematical ideas related to the construction of such fractals as Koch's curve. EJS is used to create a hand's on activity that allows a reader to create a coastline with a rubberband, six-sided die, and thumb tacks. Java applications allow for exploration of these algorithms and the influence of their associated parameters. After discussing 2D fractal mountains, this article extends the 2D algorithm to produce 3D mountains. Finally, mathematical issues in random number generation are discussed. More specifically, linear congruential generators are considered and shown to be suitable as a random number generator for the 3D fractal landscape algorithm. The use of fractal landscapes in movies is also discussed.

How Easy is 'Easy Java Simulations' Programming?

Sun, 20 Sep 2009 21:26:37 EST

How Easy is 'Easy Java Simulations' Programming?<\it> was written by mathematics professor Tim Chartier and his student Erich Kreutzer to introduce and review EJS for the MAA Mathematical Sciences Digital Library. The artticle discuss its striking benefits and also its limitations and explains how EJS can do the heavy-lifting of adding graphical user interfaces (GUIs) to your computer programs.

Blackbody Radiation Spectrum Model

Sun, 20 Sep 2009 21:21:55 EST

The Blackbody Radiation Spectrum model shows six fixed-temperature curves between Tmin and Tmax and a red variable-temperature curve that can be adjusted using a slider. The wavelength is measured in nm (nanometer) and the intensity is measured in W.e-5 / (m2.nm). Users can adjust Tmin and Tmax to change the temperature range that is displayed. The Blackbody Radiation Spectrum was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double click the ejs_ntnu_BlackbodyRadiationSpectrum.jar file to run the program if Java is installed.

CSM Textbook Chapter 3: Simulating Particle Motion

Sun, 20 Sep 2009 21:18:27 EST

Chapter 3 discusses several numerical methods needed to simulate the motion of particles using Newton's laws and introduces the Ordinary Differential Equation (ODE) editor that makes it possible to select different numerical algorithms for ODE-based models. EJS 3D elements are also introduced to model motion in three dimensions.

CSM Textbook Chapter 4: Oscillations

Sun, 20 Sep 2009 21:17:59 EST

Chapter 4 explores the behavior of oscillatory systems, including the simple harmonic oscillator, a simple pendulum, and electrical circuits and we introduce the concept of phase space. We also show how the EJS ODE editor is used to solve arrays of differential equations.

Double Pendulum Model

Sun, 20 Sep 2009 21:17:23 EST

The Double Pendulum model displays the motion of a double pendulum and its Poincare map. A double pendulum is a pendulum with another pendulum attached to its end and the state of this dynamical system is specified by two angles and two angular velocities. Because there is no fiction, the double pendulum is an example of a Hamiltonian system and energy is conserved. This EJS model simplifies the system by using equal length arms and masses. Clicking in the Poincare section sets the initial conditions of the rotor. You can examine and modify this simulation if you have EJS installed by right-clicking within the plot and selecting “Open EJS Model” from the pop-up menu item. The Double Pendulum model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_lagrangian_DoublePendulum.jar file will run the program if Java is installed. EJS is a part of the Open Source Physics Project and is designed to make it easier to access, modify, and generate computer models.

Leveraging Easy Java Simulation for High School Curriculum

Sun, 20 Sep 2009 21:16:33 EST

This paper highlights the diverse possibilities in the rich community of educators from the Conceptual Learning of Science (CoLoS) and Open Source Physics (OSP) movement to engage, enable and empower educators and students, to create interactive digital media through computer modeling. This concept revolves around a paradigmatic shift towards participatory learning through immersive computer modeling, as opposed to using technology for information transmission.

CSM Textbook Chapter 2: Creating simulations

Sun, 20 Sep 2009 21:10:07 EST

Chapter 2 introduces Java syntax and EJS elements in the context of simulating the motion of falling particles near the Earth's surface. A simple Euler algorithm for solving first-order differential equations numerically is discussed and this algorithm is shown to produce errors when compared to an analytic solution.

Blacksmithing, Introductory Physics, and Computer Programming - Slides and Code Supplement

Sun, 20 Sep 2009 21:05:31 EST

This python program simulates heat flow within an iron bar. The physical context is the heating of iron in a blacksmith's shop. The simulation is intended to accompany the preprint.

Numerical Methods for Physics, 2nd Ed.

Sun, 20 Sep 2009 20:59:21 EST

Numerical Methods for Physics is an upper-division/graduate level textbook on computational physics. The book's website provides errata, additional exercises, and information on the book's programs.

Solving Ordinary Differential Equations

Sun, 20 Sep 2009 20:58:14 EST

EJS and OSP examples to accompany the Solving Ordinary Differential Equations chapter in the Handbook of Dynamical Systems edited by Paul Fishwick. Dynamic models are described in the chapter with a “computer science slant” toward the problems of model design, representation, and analysis. EJS and OSP implementations are distributed in two ready-to-run Launcher packages.

Function Visualizer Model

Sun, 20 Sep 2009 20:48:51 EST

The Function Visualizer Model displays the graph of a function f(x) with arbitrary parameters. The function can contain polynomial, trigonometric, and exponential expressions as well a parameters. Parameters are connected to sliders that can be adjusted to observe the effect of varying parameter values. This applet was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run Java archive. Double clicking the ejs_math_FunctionVisualizer.jar file will run the program if Java is installed. EJS is a part of the Open Source Physics Project and is available in the OSP Collection.

Two-Color Multiple Slit Diffraction

Sun, 14 Jun 2009 17:44:09 EST

The Two-Color Multiple Slit Diffraction Model allows users to explore multiple slit diffraction by manipulating characteristics of the aperture and incident light to observe the resulting intensity. An exploration of resolving power in spectroscopy is included in the model. The Two-Color Multiple Slit Diffraction Model was created by Michael Gallis using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. You can examine and modify this compiled EJS model if you run the model (double click on the model's jar file), right-click within a plot, and select "Open Ejs Model" from the pop-up menu. You must, of course, have EJS installed on your computer.

Body With Thruster Model

Sun, 14 Jun 2009 17:42:27 EST

The Body with Thruster Model shows the motion of a disk with an attached rocket engine. You can drag the engine to change its distance from the center of the disk and you can adjust the thrust of the rocket engine using sliders. The mass of the rocket and its connecting rod are assumed to be negligible. The trajectory of this single-body model is intuitively challenging and difficult to visualize. The Body with Thruster Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_mech_newton_BodyWithThruster.jar file will run the program if Java is installed.

Charge in Magnetic Field Model

Sun, 14 Jun 2009 17:41:55 EST

The EJS Charge In B-Field model allows the user to simulate moving charged particles in two identical magnetic field regions separated by a zero magnetic field gap. The Charge in B Field Model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ntnu_em_ChargeInBField.jar file will run the program if Java is installed.

Helmholtz Coils

Sun, 14 Jun 2009 17:41:11 EST

The EJS Helmholtz Coils Model shows a the magnetic field between two circular coils of wire. The default configuration, known as a Helmholtz coil, sets the separation distance D equal to the coil radius R. These values produce a nearly uniform magnetic field B between the coils The Helmholtz Coils Model was created using the Easy Java Simulations (Ejs) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_ntnu_em_HelmholtzCoils.jar file will run the program if Java is installed.

Linear Congruent Number Generator

Sun, 14 Jun 2009 17:40:44 EST

The Linear Congruent Number Generator Model The method generates a sequence of integers xi over the interval [0, m-1] by the recurrence relation x[i+1] = (ax[i]+c) mod m where the modulus m is greater than zero, the multiplier a is greater than zero and less than m, and the increment c is greater than zero and less than m. All numbers are integers and all arithmetic is integer arithmetic. The initial value x0 is known as the seed. The Linear Congruent Number Generator Model was created using the Easy Java Simulations (EJS) modeling tool. It is distributed as a ready-to-run (compiled) Java archive. Double clicking the ejs_math_RandomLCG.jar file will run the program if Java is installed.