Students learn about complex networks and how to use graphs to represent them. They also learn that graph theory is a useful part of mathematics for studying complex networks in diverse applications of science and engineering, including neural networks in the brain, biochemical reaction networks in cells, communication networks, such as the internet, and social networks. Students are also introduced to random processes on networks. An illustrative example shows how a random process can be used to represent the spread of an infectious disease, such as the flu, on a social network of students, and demonstrates how scientists and engineers use mathematics and computers to model and simulate random processes on complex networks for the purposes of learning more about our world and creating solutions to improve our health, happiness and safety.

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Quantitative techniques of operations research with emphasis on applications in transportation systems analysis (urban, air, ocean, highway, and pickup and delivery systems) and in the planning and design of logistically oriented urban service systems (e.g., fire and police departments, emergency medical services, and emergency repair services). Unified study of functions of random variables, geometrical probability, multi-server queuing theory, spatial location theory, network analysis and graph theory, and relevant methods of simulation. Computer exercises and discussions of implementation difficulties.

This is an interactive 3-D simulation of the electric field of two equal and opposite charges. The user moves an observation point around to see how the total field at various points arises from the individual fields of each charge. This item is part of a larger collection of visualizations developed by the MIT TEAL/Studio Physics Project to support an introductory course in electricity and magnetism. Lecture notes, labs, and presentations are also available as part of the MIT Open Courseware Repository: MIT Open Courseware: Electricity and Magnetism

Maneuvering motions of surface and underwater vehicles. Derivation of equations of motion, hydrodynamic coefficients. Memory effects. Linear and nonlinear forms of the equations of motion. Control surfaces modeling and design. Engine, propulsor, and transmission systems modeling and simulation during maneuvering. Stability of motion. Principles of multivariable automatic control. Optimal control, Kalman filtering, loop transfer recovery. Term project: applications chosen from autopilots for surface vehicles; towing in open seas; remotely operated vehicles.

This course covers the mathematical techniques necessary for understanding of materials science and engineering topics such as energetics, materials structure and symmetry, materials response to applied fields, mechanics and physics of solids and soft materials. The class uses examples from the materials science and engineering core courses (3.012 and 3.014) to introduce mathematical concepts and materials-related problem solving skills. Topics include linear algebra and orthonormal basis, eigenvalues and eigenvectors, quadratic forms, tensor operations, symmetry operations, calculus of several variables, introduction to complex analysis, ordinary and partial differential equations, theory of distributions, and fourier analysis. Users may find additional or updated materials at Professor Carter's 3.016 course Web site.

A collaboration between the National Aeronautics and Space Administration (NASA) and the CK-12 Foundation, this book provides high school mathematics and physics teachers with an introduction to the main principles of modeling and simulation used in science and engineering. An appendix of lesson plans is included.

This simulation is about Motion with Constant Acceleration

هذه المحاكاة تشرح عن الحركة مع التسارع المستمر

This simulation explores the relationship between particle kinetic energies during particle collisions. It is used in Lesson 13 of Unit 6.2 in the OpenSciEd curriculum.

Students apply concepts of disease transmission to analyze infection data, either provided or created using Bluetooth-enabled Android devices. This data collection may include several cases, such as small static groups (representing historically rural areas), several roaming students (representing world-travelers), or one large, tightly knit group (representing urban populations). To explore the algorithms to a deeper degree, students may also design their own diseases using the App Inventor framework.

Play with one or two pendulums and discover how the period of a simple pendulum depends on the length of the string, the mass of the pendulum bob, and the amplitude of the swing. It's easy to measure the period using the photogate timer. You can vary friction and the strength of gravity. Use the pendulum to find the value of g on planet X. Notice the anharmonic behavior at large amplitude.

Building on their understanding of graphs, students are introduced to random processes on networks. They walk through an illustrative example to see how a random process can be used to represent the spread of an infectious disease, such as the flu, on a social network of students. This demonstrates how scientists and engineers use mathematics to model and simulate random processes on complex networks. Topics covered include random processes and modeling disease spread, specifically the SIR (susceptible, infectious, resistant) model.

This simulation is about Projectile Motion set initial velocity components

هذه المحاكاة تتعلق بحركة المقذوفات - وآلية تحديد مكونات السرعه الأولية.

This simulation is about Projectile Motion set speed and angle. هذه المحاكاة تتعلق بحركة المقذوفات - السرعه والزاوية

This simulation is about Projectile Motion with motion diagram and velocity components

, هذه المحاكاة تتحدث عن - حركة المقذوفات , مع عناصر الرسم البياني الحركة والسرعه.

This simulation is about Projectile Motion (with motion diagram, velocity components, and graphs,

هذه المحاكاة هي تتحدث عن حركة المقذوفات ومايتعلق بمخطط الحركة، مكوناته والسرعة، والرسوم البيانية

This simulation is showing the Race between a dropped ball and one launched horizontally هذه المحاكاة توضح الفرق بالسرعه بين كرة سقطت من الأعلى الى الأسفل وبين كرة اطلقت من الأسفل الى الأعلى.

Principles of thermal radiation and their application to engineering heat and photon transfer problems. Quantum and classical models of radiative properties of materials, electromagnetic wave theory for thermal radiation, radiative transfer in absorbing, emitting, and scattering media, and coherent laser radiation. Applications cover laser-material interactions, imaging, infrared instrumentation, global warming, semiconductor manufacturing, combustion, furnaces, and high temperature processing.

This simulation involves relative velocity in one dimension. It is an out-and-back race between two women. Mia runs on the moving sidewalk, while Brandi runs on the non-moving floor. Under what conditions is the race a tie? Under what conditions does Mia win? Under what conditions does Brandi win?

Students explore the definition and interpretations of the probability of an event by investigating the long run proportion of times a sum of 8 is obtained when two balanced dice are rolled repeatedly. Making use of hand calculations, computer simulations, and descriptive techniques, students encounter the laws of large numbers in a familiar setting. By working through the exercises, students will gain a deeper understanding of the qualitative and quantitative relationships between theoretical probability and long run relative frequency. Particularly, students investigate the proximity of the relative frequency of an event to its probability and conclude, from data, that the dispersion of the relative frequency diminishes on the order .