This activity leads students to appreciate the usefulness of simulations for approximating probabilities. It also provides them with experience calculating probabilities based on geometric arguments and using the bivariate normal distribution. We have used it in courses in probability and mathematical statistics, as well as in an introductory statistics course at the post-calculus level.

In this simulation, you see, on the left, a picture of a box at rest on a table. You can apply a force to the box - note that you set the y-component and the x-component separately. On the right, you can see the full free-body diagram of the box. The free-body diagram shows the gravitational force exerted on the box by the Earth, the normal force exerted by the table, the force that you apply, and, if there is one, the static force of friction. Note that, on the free-body diagram, the force of gravity and the normal force have been shifted horizontally a little so they can be seen more easily. If there is a net force, that is also indicated.

Survey of optimization methods for management of water resources. Linear, integer, nonlinear, and dynamic programming illustrated with case studies. Applications include reservoir and irrigation development, conjunctive use of surface and groundwater, capacity expansion, and sustainable resource development. This subject is concerned with quantitative methods for analyzing large-scale water resource problems. Topics covered include the design and management of facilities for river basin development, flood control, water supply, groundwater remediation, and other activities related to water resources. Simulation models and optimization methods are often used to support analyses of water resource problems. In this subject we will be constructing simulation models with the MATLABĺ¨ programming language and solving numerical optimization problems with the GAMS optimization package.

The simulation shows different ways of looking at position and velocity vectors for a ball experiencing projectile motion.

تبين المحاكاة طرق مختلفة للنظر في الموقف وسرعة النقل لحركة المقذوفات

The simulation shows the classic physics situation of a monkey and hunter.
In this case, the hunter is trying to tranquilize the monkey, so the monkey can be re-located to a better habitat. The monkey is clever - when the tranquilizer dart (in blue) leaves the gun, the monkey (in purple) lets go of the tree branch, and starts to fall straight down. Note that there is a net (not shown) at the bottom to catch the monkey, so the monkey won't get hurt.
How should the gun be aimed so the dart hits the monkey?

You can explore various parameters, including changing the direction the gun is aimed, changing the value of the acceleration due to gravity, and adjusting the dart's launch speed.

In this simulation, you see, on the left, a picture of a box at rest on a table. You can apply a vertical force (up or down) to the box. On the right, you can see the full free-body diagram of the box. The free-body diagram shows the gravitational force (green) exerted on the box by the Earth, the normal force (purple) exerted by the table, and the vertical force (dark blue) that you apply. Note that, on the free-body diagram, all three forces are along the vertical line passing through the center of the box, but the force of gravity and the normal force have been shifted a little so they can be seen more easily.

هذه المحاكاة تتحدث عن القوة الطبيعية في الفيزياء