Online courses directory (19947)

Material covered in this course includes the following topics:

• Laws of thermodynamics: general formulation and applications to mechanical, electromagnetic and electrochemical systems, solutions, and phase diagrams
• Computation of phase diagrams
• Statistical thermodynamics and relation between microscopic and macroscopic properties, including ensembles, gases, crystal lattices, phase transitions
• Applications to phase stability and properties of mixtures
• Computational modeling
• Interfaces

This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5111 (Materials at Equilibrium).

Here we will learn about the mechanical behavior of structures and materials, from the continuum description of properties to the atomistic and molecular mechanisms that confer those properties to all materials. We will cover elastic and plastic deformation, creep, fracture and fatigue of materials including crystalline and amorphous metals, semiconductors, ceramics, and (bio)polymers, and will focus on the design and processing of materials from the atomic to the macroscale to achieve desired mechanical behavior. We will cover special topics in mechanical behavior for material systems of your choice, with reference to current research and publications.

This course uses the theory and application of atomistic computer simulations to model, understand, and predict the properties of real materials. Specific topics include: energy models from classical potentials to first-principles approaches; density functional theory and the total-energy pseudopotential method; errors and accuracy of quantitative predictions: thermodynamic ensembles, Monte Carlo sampling and molecular dynamics simulations; free energy and phase transitions; fluctuations and transport properties; and coarse-graining approaches and mesoscale models. The course employs case studies from industrial applications of advanced materials to nanotechnology. Several laboratories will give students direct experience with simulations of classical force fields, electronic-structure approaches, molecular dynamics, and Monte Carlo.

This course was also taught as part of the Singapore-MIT Alliance (SMA) programme as course number SMA 5107 (Atomistic Computer Modeling of Materials).

Acknowledgements

Support for this course has come from the National Science Foundation's Division of Materials Research (grant DMR-0304019) and from the Singapore-MIT Alliance.

Discusses a wide variety of processes and materials from the viewpoint of their fundamental physical and chemical properties. Specific topics: cold welding, adhesive bonding, diffusion bonding, soldering, brazing, flames, arcs, high-energy density heat sources, solidification, cracking resistance, shielding methods, and electric contacts. Emphasis on underlying science of a given process rather than a detailed description of the technique or equipment.

This course meets with the first half of 3.371J in the Fall Term.

This course will cover the following topics:

• Magnetostatics
• Origin of magnetism in materials
• Magnetic domains and domain walls
• Magnetic anisotropy
• Reversible and irreversible magnetization processes
• Hard and soft magnetic materials
• Magnetic recording

Special topics include magnetism of thin films, surfaces and fine particles; transport in ferromagnets, magnetoresistive sensors, and amorphous magnetic materials.

This course covers the theory, design, fabrication and applications of photonic materials and devices. After a survey of optical materials design for semiconductors, dielectrics and polymers, the course examines ray optics, electromagnetic optics and guided wave optics; physics of light-matter interactions; and device design principles of LEDs, lasers, photodetectors, modulators, fiber and waveguide interconnects, optical filters, and photonic crystals. Device processing topics include crystal growth, substrate engineering, thin film deposition, etching and process integration for dielectric, silicon and compound semiconductor materials. The course also covers microphotonic integrated circuits and applications in telecom/datacom systems. Course assignments include four design projects that emphasize materials, devices and systems applications.

This course covers a variety of topics concerning superconducting magnets, including thermodynamic and transport properties of aqueous and nonaqueous electrolytes, the electrode/electrolyte interface, and the kinetics of electrode processes. It also covers electrochemical characterization with regards to d.c. techniques (controlled potential, controlled current) and a.c. techniques (voltametry and impedance spectroscopy). Applications of the following will also be discussed: electrowinning, electrorefining, electroplating, and electrosynthesis, as well as electrochemical power sources (batteries and fuel cells).

One objective of 15.066J is to introduce modeling, optimization and simulation, as it applies to the study and analysis of manufacturing systems for decision support. The introduction of optimization models and algorithms provide a framework to think about a wide range of issues that arise in manufacturing systems. The second objective is to expose students to a wide range of applications for these methods and models, and to integrate this material with their introduction to operations management.

This course is aimed at presenting the concepts underlying the response of polymeric materials to applied loads. These will include both the molecular mechanisms involved and the mathematical description of the relevant continuum mechanics. It is dominantly an "engineering" subject, but with an atomistic flavor. It covers the influence of processing and structure on mechanical properties of synthetic and natural polymers: Hookean and entropic elastic deformation, linear viscoelasticity, composite materials and laminates, yield and fracture.

Analysis I (18.100) in its various versions covers fundamentals of mathematical analysis: continuity, differentiability, some form of the Riemann integral, sequences and series of numbers and functions, uniform convergence with applications to interchange of limit operations, some point-set topology, including some work in Euclidean n-space.

MIT students may choose to take one of three versions of 18.100: Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible. Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology. Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication.

This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs. MIT students may choose to take one of three versions of Real Analysis; this version offers three additional units of credit for instruction and practice in written and oral presentation.

The three options for 18.100:

• Option A (18.100A) chooses less abstract definitions and proofs, and gives applications where possible.
• Option B (18.100B) is more demanding and for students with more mathematical maturity; it places more emphasis from the beginning on point-set topology and n-space, whereas Option A is concerned primarily with analysis on the real line, saving for the last weeks work in 2-space (the plane) and its point-set topology.
• Option C (18.100C) is a 15-unit variant of Option B, with further instruction and practice in written and oral communication. This fulfills the MIT CI requirement.

Teaches creative design based on the scientific method through the design, engineering, and manufacture of a detailed inlaid tile. This is an introductory lecture/studio course designed to teach students the basic principles of design and expose them to the design process. Throughout the course, students will be introduced to the terminology and concepts that underlie all forms of visual art; which--in many ways--forms the basis for the design of all physical objects. Along with learning mechanical skills, thinking both critically and visually, and working with different media, the students will consider how the arts grow out of and respond to particular cultural contexts and ideas; and how these thinking patterns can be applied to virtually all types of design.

Presentations, lectures, demonstrations, discussions and various artistic works will be used to show students how other artists and designers have dealt with the same issues they will be facing in lab.  Each class will begin with a critique of the students' homework, followed by a discussion (and presentation when appropriate) of the pertinent issues of that week. All aspects of the course will aid the teams of students in designing and building a major inlaid tile whose elements are designed as digital solid models and manufactured on an abrasive waterjet machining center. The course will conclude with an exhibit of the completed tiles open to the MIT and the Greater-Boston public. Enrollment is limited to 16 students who will be divided into groups of 4 students each. Preference will be given to students who attend the first day of class in a pre-selected team of 4.

18.311 Principles of Continuum Applied Mathematics covers fundamental concepts in continuous applied mathematics, including applications from traffic flow, fluids, elasticity, granular flows, etc. The class also covers continuum limit; conservation laws, quasi-equilibrium; kinematic waves; characteristics, simple waves, shocks; diffusion (linear and nonlinear); numerical solution of wave equations; finite differences, consistency, stability; discrete and fast Fourier transforms; spectral methods; transforms and series (Fourier, Laplace). Additional topics may include sonic booms, Mach cone, caustics, lattices, dispersion, and group velocity.

This course offers a rigorous treatment of linear algebra, including vector spaces, systems of linear equations, bases, linear independence, matrices, determinants, eigenvalues, inner products, quadratic forms, and canonical forms of matrices. Compared with 18.06 Linear Algebra, more emphasis is placed on theory and proofs.

In this undergraduate level seminar series, topics vary from year to year. Students present and discuss the subject matter, and are provided with instruction and practice in written and oral communication. Some experience with proofs required. The topic for fall 2008: Computational algebra and algebraic geometry.

The subject of enumerative combinatorics deals with counting the number of elements of a finite set. For instance, the number of ways to write a positive integer n as a sum of positive integers, taking order into account, is 2^n-1. We will be concerned primarily with bijective proofs, i.e., showing that two sets have the same number of elements by exhibiting a bijection (one-to-one correspondence) between them. This is a subject which requires little mathematical background to reach the frontiers of current research. Students will therefore have the opportunity to do original research. It might be necessary to limit enrollment.

This course provides a review of linear algebra, including applications to networks, structures, and estimation, Lagrange multipliers. Also covered are: differential equations of equilibrium; Laplace's equation and potential flow; boundary-value problems; minimum principles and calculus of variations; Fourier series; discrete Fourier transform; convolution; and applications.

Note: This course was previously called "Mathematical Methods for Engineers I."

This course emphasizes concepts and techniques for solving integral equations from an applied mathematics perspective. Material is selected from the following topics: Volterra and Fredholm equations, Fredholm theory, the Hilbert-Schmidt theorem; Wiener-Hopf Method; Wiener-Hopf Method and partial differential equations; the Hilbert Problem and singular integral equations of Cauchy type; inverse scattering transform; and group theory. Examples are taken from fluid and solid mechanics, acoustics, quantum mechanics, and other applications.

This course offers an advanced introduction to numerical linear algebra. Topics include direct and iterative methods for linear systems, eigenvalue decompositions and QR/SVD factorizations, stability and accuracy of numerical algorithms, the IEEE floating point standard, sparse and structured matrices, preconditioning, linear algebra software. Problem sets require some knowledge of MATLAB®.

Find out what solid-state physics has brought to Electromagnetism in the last 20 years. This course surveys the physics and mathematics of nanophotonics—electromagnetic waves in media structured on the scale of the wavelength.

Topics include computational methods combined with high-level algebraic techniques borrowed from solid-state quantum mechanics: linear algebra and eigensystems, group theory, Bloch's theorem and conservation laws, perturbation methods, and coupled-mode theories, to understand surprising optical phenomena from band gaps to slow light to nonlinear filters.

Note: An earlier version of this course was published on OCW as 18.325 Topics in Applied Mathematics: Mathematical Methods in Nanophotonics, Fall 2005.