A comprehensive treatment of the theory of partial differential equations (pde) from an applied mathematics perspective. Equilibrium, propagation, diffusion, and other phenomena. Initial and boundary value problems. Transform methods, eigenvalue and eigenfunction expansions, Green's functions. Theory of characteristics and shocks. Boundary layers and other singular perturbation phenomena. Elementary concepts for the numerical solution of pde's. Illustrative examples from fluid dynamics, nonlinear waves, geometrical optics, and other applications.

This case is based on an actual article entitled "Baby Alert" that appeared in Consumer Reports (May 1999). The article raises some concerns about the safety of polycarbonate baby bottles, and recommends that parents dispose of them as a precaution. However, the American Plastics Council and the Food and Drug Administration have raised concerns about the experimental methodology used as well as the recommendations made in this article. The case has been used to help develop students' critical thinking skills in an introductory chemistry course for non-majors. It may be used to illustrate applications in polymer chemistry, quantitative chemical analysis, toxicology, endocrine disruption, and risk-benefit analysis.

This course will focus on providing students with the tools needed to practice responsible architecture in a contemporary context. It will familiarize students with the materials currently used in responsible practice, as well as the material properties most relevant to assembly. The course will also introduce students to materials that are untested but hold promise for future usage. Finally, the course will challenge students to refine their understanding of responsible or sustainable design practice by looking at the evolution of those ideas within the field of architecture.

The goal is for students to understand the basics of engineering that go into the design of a sneaker. The bottom or sole of a sneaker provides support, cushioning, and traction. In addition the sole is flexible and can have some fashion based functions such as cool colors and added height. The sneaker is a well-engineered product, utilizing a variety of materials to create a highly functional, useful shoe. This unit focuses on having the students select specific design requirements, such as good traction or lots of cushioning, and then select from a variety of materials to build a model shoe with the same design criteria.

Students learn about the periodic table and how pervasive the elements are in our daily lives. After reviewing the table organization and facts about the first 20 elements, they play an element identification game. They also learn that engineers incorporate these elements into the design of new products and processes. Acting as computer and animation engineers, students creatively express their new knowledge by creating a superhero character based on of the elements they now know so well.

The goal is for students to understand the basics of engineering associated with the use, selection, and properties of fabrics. A wide variety of natural and synthetic fibers are used in our clothing, home furnishings and in our travel and sports equipment. The specific material chosen for each application depends on how closely the properties of the material match the design needs. This unit focuses on the different characteristics of fabrics and shows students how natural and synthetic fabrics differ from one another. It also shows students the opportunity to weigh the advantages and disadvantages of fabrics when considering the appropriate fabric to be used.

This subject describes the fundamentals of bonding, energetics, and structure that underpin materials science. From electrons to silicon to DNA: the role of electronic bonding in determining the energy, structure, and stability of materials. Quantum mechanical descriptions of interacting electrons and atoms. Symmetry properties of molecules and solids. Structure of complex and disordered materials. Introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to molecular models of materials. Develops basis for understanding a broad range of materials phenomena, from heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism. Fundamentals are taught using real-world examples such as engineered alloys, electronic and magnetic materials, ionic and network solids, polymers, and biomaterials.

Basic concepts of computer modeling in science and engineering using discrete particle systems and continuum fields. Techniques and software for statistical sampling, simulation, data analysis and visualization. Use of statistical, quantum chemical, molecular dynamics, Monte Carlo, mesoscale and continuum methods to study fundamental physical phenomena encountered in the fields of computational physics, chemistry, mechanics, materials science, biology, and applied mathematics. Applications drawn from a range of disciplines to build a broad-based understanding of complex structures and interactions in problems where simulation is on equal-footing with theory and experiment. Term project allows development of individual interest. Student mentoring by a coordinated team of participating faculty from across the Institute.

The class will cover 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 3.012 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, fourier analysis and random walks.

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.

Mechanics studies how forces affect bodies in motion--how, for example, a bullet is fired from a gun, or a top is set in motion by the flick of a wrist. This course will introduce the student to the core concepts of mechanics as applied to design, testing, and manufacture of safe and reliable products. Upon successful completion of this course, the student will be able to: Identify and use units, notations, and vectors used in mechanics; Identify and explain the concepts of forces, couples, and moments; Use the concept of forces and moments to compute resultants and equivalent systems in mechanics; Analyze mechanics of rigid bodies, such as trusses, frames, and machines; Identify and explain the concepts of friction and internal forces; Compute material properties of solid bodies, such as moments of inertia and mass moments of inertia; Compute strain and stress and understand the relationship of stress and strain for both elastic and plastic bodies; Compute stresses and strain in bodies subjected to tension and torsion; Compute stresses and strain in pressure vessels and composites; Identify and explain the concept of stress tensor and the constitutive relationship between strain and stress; Compute stresses and strain in simple and composite beams due to bending; Explain how stress is computed experimentally or using finite element formulations; Identify and explain material failure scenarios, such as fracture, fatigue, creep, and buckling. (Mechanical Engineering 102)

Introduction to continuum mechanics and material modeling of engineering materials based on first energy principles: deformation and strain; momentum balance, stress and stress states; elasticity and elasticity bounds; plasticity and yield design. Overarching theme is a unified mechanistic language using thermodynamics, which allows understanding, modeling and design of a large range of engineering materials.

Analysis and design at a molecular scale of materials used in contact with biological systems, including biotechnology and biomedical engineering. Topics include molecular interactions between bio- and synthetic molecules and surfaces; design, synthesis, and processing approaches for materials that control cell functions; and application of state-of-the-art materials science to problems in tissue engineering, drug delivery, biosensors, and cell-guiding surfaces.

Analysis and design at a molecular scale of materials used in contact with biological systems, including biotechnology and biomedical engineering. Topics include molecular interactions between bio- and synthetic molecules and surfaces; design, synthesis, and processing approaches for materials that control cell functions; and application of state-of-the-art materials science to problems in tissue engineering, drug delivery, biosensors, and cell-guiding surfaces.

Cement production may be classified by application into two primary groups: construction and energy services. The construction applications for cementing consume the lion’s share of cement manufactured world-wide, but the cement produced for energy services applications is an integral part of meeting the world’s energy needs and requires tighter quality control standards to meet that industry’s higher demands on control of the rheological properties of the fluid slurry state, the solid state, and especially the transition from the former state to the latter, or the setting process. Applications relating to the energy services industry are the primary focus of this work. Additionally, cement may also become central to efforts in nuclear waste management by locking radioactive material within the cementitious matrix, where rates of diffusion of waste out of the cement serve as the dominant concern. These modules explain the chemistry of Portland cement and its applications for the energy industry.

Students are given a variety of materials and asked to identify if each material as a solid, liquid or gas. They use their five senses sight, sound, smell, texture and taste to identify the other characteristics of each item.