This course covers the classical partial differential equations of applied mathematics: diffusion, Laplace/Poisson, and wave equations. It also includes methods and tools for solving these PDEs, such as separation of variables, Fourier series and transforms, eigenvalue problems, and Green’s functions.

This course provides students with the basic analytical and computational tools of linear partial differential equations (PDEs) for practical applications in science engineering, including heat / diffusion, wave, and Poisson equations. Analytics emphasize the viewpoint of linear algebra and the analogy with finite matrix problems. Numerics focus on finite-difference and finite-element techniques to reduce PDEs to matrix problems. The Julia Language (a free, open-source environment) is introduced and used in homework for simple examples.

This course discusses the basics every manager needs to organize successful technology-driven innovation in both entrepreneurial and established firms. We start by examining innovation-based strategies as a source of competitive advantage and then examine how to build organizations that excel at identifying, building and commercializing technological innovations. Major topics include how the innovation process works; creating an organizational environment that rewards innovation and entrepreneurship; designing appropriate innovation processes (e.g. stage-gate, portfolio management); organizing to take advantage of internal and external sources of innovation; and structuring entrepreneurial and established organizations for effective innovation. The course examines how entrepreneurs can shape their firms so that they continuously build and commercialize valuable innovations. Many of the examples also focus on how established firms can become more entrepreneurial in their approach to innovation.

Insert channels in a membrane and see what happens. See how different types of channels allow particles to move through the membrane.

Insert channels in a membrane and see what happens. See how different types of channels allow particles to move through the membrane.

The real structure of cell membrane is so dynamic & it not only allows the cells to move but also has constant movement & fluidity. Therefore, an animation would be great for teaching the dynamic movement of phospholipids & proteins in cell membrane. This LO also helps students to understand the movement of material across the membrane. I prefer students watch it at least twice.

This course introduces the theory and technology of micro/nano fabrication. Lectures and laboratory sessions focus on basic processing techniques such as diffusion, oxidation, photolithography, chemical vapor deposition, and more. Through team lab assignments, students are expected to gain an understanding of these processing techniques, and how they are applied in concert to device fabrication. Students enrolled in this course have a unique opportunity to fashion and test micro/nano-devices, using modern techniques and technology.

This course models multi-domain engineering systems at a level of detail suitable for design and control system implementation. Topics include network representation, state-space models; multi-port energy storage and dissipation, Legendre transforms; nonlinear mechanics, transformation theory, Lagrangian and Hamiltonian forms; and control-relevant properties. Application examples may include electro-mechanical transducers, mechanisms, electronics, fluid and thermal systems, compressible flow, chemical processes, diffusion, and wave transmission.

Today, computer-based simulations are becoming increasingly popular, especially when daylighting and energy conservation are amongst the key goals for a project. This two-week workshop will expose participants to the current daylighting simulation models and beyond, by introducing realistic and dynamic assessment methods through hands-on exercises and application to a design project. Open to students and practitioners.
This course is offered during the Independent Activities Period (IAP), which is a special 4-week term at MIT that runs from the first week of January until the end of the month.

This course introduces the structure, composition, and physical processes governing the terrestrial planets, including their formation and basic orbital properties. Topics include plate tectonics, earthquakes, seismic waves, rheology, impact cratering, gravity and magnetic fields, heat flux, thermal structure, mantle convection, deep interiors, planetary magnetism, and core dynamics. Suitable for majors and non-majors seeking general background in geophysics and planetary structure.

"This course introduces the structure, composition, and physical processes governing the terrestrial planets, including their formation and basic orbital properties. Topics include plate tectonics, earthquakes, seismic waves, rheology, impact cratering, gravity and magnetic fields, heat flux, thermal structure, mantle convection, deep interiors, planetary magnetism, and core dynamics. Suitable for majors and non-majors seeking general background in geophysics and planetary structure."

Discuss the roles of both high culture and pop culture within societyDifferentiate between subculture and countercultureExplain the role of innovation, invention, and discovery in cultureUnderstand the role of cultural lag and globalization in cultural change

This activity is designed to give students an understanding of one aspect of what an engineer does and the ability to experience various steps in the engineering design process as it relates to a 3D printing task. Students transform into engineers as they work in teams to carry out a 3D printing task by using a blunt-tip needle syringe to print a line using a variety of colored liquid materials (shampoo, conditioner, aloe, and hand sanitizer) into a small plastic box filled with a gel base. Approximating the work of engineers, the teams observe the interactions between the printed material and the gel base at intervals of 10 minutes and iterate, or change, the ink base as necessary to achieve a goal. Using the dye to color the ink allows students to determine which material will permeate or diffuse throughout the base more effectively. Teams share their results to compare with their classmates. A real-world application for this investigation would be when engineers conduct research to develop new medicines, the goal is for the medicine to make its way through the body in the most effective way so that the body can heal.

This course is a project-based introduction to manipulating and characterizing cells and biological molecules using microfabricated tools. It is designed for first year undergraduate students. In the first half of the term, students perform laboratory exercises designed to introduce (1) the design, manufacture, and use of microfluidic channels, (2) techniques for sorting and manipulating cells and biomolecules, and (3) making quantitative measurements using optical detection and fluorescent labeling. In the second half of the term, students work in small groups to design and test a microfluidic device to solve a real-world problem of their choosing. Includes exercises in written and oral communication and team building.

In this subject, we consider two basic topics in cellular biophysics, posed here as questions:

Which molecules are transported across cellular membranes, and what are the mechanisms of transport? How do cells maintain their compositions, volume, and membrane potential?
How are potentials generated across the membranes of cells? What do these potentials do?

Although the questions posed are fundamentally biological questions, the methods for answering these questions are inherently multidisciplinary. As we will see throughout the course, the role of mathematical models is to express concepts precisely enough that precise conclusions can be drawn. In connection with all the topics covered, we will consider both theory and experiment. For the student, the educational value of examining the interplay between theory and experiment transcends the value of the specific knowledge gained in the subject matter.
This course is jointly offered through four departments, available to both undergraduates and graduates.

Students learn that engineers develop different polymers to serve various functions and are introduced to selectively permeable membranes. In a warm-up activity, they construct models of selectively permeable membranes using common household materials, and are reminded about simple diffusion and passive transport. In the main activity, student pairs test and compare the selective permeability of everyday polymer materials engineered for food storage (including plastic grocery bags, zipper sandwich bags, and plastic wrap) with various in-solution molecules (iodine, corn starch, food coloring, marker dye), assess how the polymer’s permeability relates to its function/purpose, and compare that to the permeability of dialysis tubing (which simulates a cell membrane).

This course covers the general principles of separation by equilibrium and rate processes. Topics include staged cascades and applications to distillation, absorption, adsorption, and membrane processes. Phase equilibria and the role of diffusion are also covered.

The purpose of 15.840 is to:

Introduce key marketing ideas and phenomena.
Develop students’ skills in marketing analysis and planning.
Provide a forum (both written and oral) for presenting and defending recommendations and critically examining and discussing those of others. An emphasis is placed on theory and practice that draws on market research, competitive analysis, and marketing science.

Students experience the engineering design process as they design, fabricate, test and redesign their own methods for encapsulation of a (hypothetical) new miracle drug. As if they are engineers, teams make large-size prototypes to test proof of concept. They use household materials (tape, paper towels, plastic wrap, weed-barrier fabric, glues, etc.) to attach a coating to a porous "shell" (a perforated plastic Wiffle® ball) containing the medicine (colored drink mix powder). The objective is to delay the drug release by a certain time and have a long release duration—patterned after the timed release requirements of many real-world pharmaceuticals that are released from a polymer shell via diffusion in the body. Guided by a worksheet, teams go through at least three design/test iterations, aiming to achieve a solution close to the target time release constraints.