# Online courses directory (13)

Designed to familiarize students with theories and analytical tools useful for studying research literature, this course is a survey of fluid mechanical problems in the water environment. Because of the inherent nonlinearities in the governing equations, we shall emphasize the art of making analytical approximations not only for facilitating calculations but also for gaining deeper physical insight. The importance of scales will be discussed throughout the course in lectures and homeworks. Mathematical techniques beyond the usual preparation of first-year graduate students will be introduced as a part of the course. Topics vary from year to year.

This course focuses on the interaction of chemical engineering, biochemistry, and microbiology. Mathematical representations of microbial systems are featured among lecture topics. Kinetics of growth, death, and metabolism are also covered. Continuous fermentation, agitation, mass transfer, and scale-up in fermentation systems, and enzyme technology round out the subject material.

This course covers the analytical, graphical, and numerical methods supporting the analysis and design of integrated biological systems. Topics include modularity and abstraction in biological systems, mathematical encoding of detailed physical problems, numerical methods for solving the dynamics of continuous and discrete chemical systems, statistics and probability in dynamic systems, applied local and global optimization, simple feedback and control analysis, statistics and probability in pattern recognition.

An official course Web site and Wiki is maintained on OpenWetWare: 20.181 Computation for Biological Engineers.

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."

Concepts in Nanotechnology is a six-week introduction to nanotechnology. The course is designed at a pre-college level, with no college level chemistry, math, or physics experience required. You will learn what nanotechnology is and what it means for something to be a nanomaterial. You will also learn about the applications and commercial products that use nanotechnology. This is an exciting opportunity to delve into the nano-world. Prerequisites: The course is taught entirely in English and aimed at a U.S. high school level. You need to be familiar with the basic concepts of chemistry, such as the theory of atoms and the periodic table of elements. Basic algebra skills, such as how to deal with equations containing variables, fractions, and exponents is necessary. No prerequisite knowledge in nanotechnology, materials science, or physics is required.

This is an advanced course on modeling, design, integration and best practices for use of machine elements such as bearings, springs, gears, cams and mechanisms. Modeling and analysis of these elements is based upon extensive application of physics, mathematics and core mechanical engineering principles (solid mechanics, fluid mechanics, manufacturing, estimation, computer simulation, etc.). These principles are reinforced via (1) hands-on laboratory experiences wherein students conduct experiments and disassemble machines and (2) a substantial design project wherein students model, design, fabricate and characterize a mechanical system that is relevant to a real world application. Students master the materials via problems sets that are directly related to, and coordinated with, the deliverables of their project. Student assessment is based upon mastery of the course materials and the student's ability to synthesize, model and fabricate a mechanical device subject to engineering constraints (e.g. cost and time/schedule).

This subject provides an introduction to the mechanics of materials and structures. You will be introduced to and become familiar with all relevant physical properties and fundamental laws governing the behavior of materials and structures and you will learn how to solve a variety of problems of interest to civil and environmental engineers. While there will be a chance for you to put your mathematical skills obtained in 18.01, 18.02, and eventually 18.03 to use in this subject, the emphasis is on the physical understanding of why a material or structure behaves the way it does in the engineering design of materials and structures.

This course focuses on the fundamentals of structure, energetics, and bonding that underpin materials science. It is the introductory lecture class for sophomore students in Materials Science and Engineering, taken with 3.014 and mathematics-for-materials-scientists-and-engineers-fall-2005/index.htm">3.016 to create a unified introduction to the subject. Topics include: an introduction to thermodynamic functions and laws governing equilibrium properties, relating macroscopic behavior to atomistic and molecular models of materials; the role of electronic bonding in determining the energy, structure, and stability of materials; quantum mechanical descriptions of interacting electrons and atoms; materials phenomena, such as heat capacities, phase transformations, and multiphase equilibria to chemical reactions and magnetism; symmetry properties of molecules and solids; structure of complex, disordered, and amorphous materials; tensors and constraints on physical properties imposed by symmetry; and determination of structure through diffraction. Real-world applications include engineered alloys, electronic and magnetic materials, ionic and network solids, polymers, and biomaterials.

This course is a core subject in MIT's undergraduate Energy Studies Minor. This Institute-wide program complements the deep expertise obtained in any major with a broad understanding of the interlinked realms of science, technology, and social sciences as they relate to energy and associated environmental challenges.

This course provides an integrated introduction to electrical engineering and computer science, taught using substantial laboratory experiments with mobile robots. Our primary goal is for you to learn to appreciate and use the fundamental design principles of modularity and abstraction in a variety of contexts from electrical engineering and computer science.

Our second goal is to show you that making mathematical models of real systems can help in the design and analysis of those systems. Finally, we have the more typical goals of teaching exciting and important basic material from electrical engineering and computer science, including modern software engineering, linear systems analysis, electronic circuits, and decision-making.

#### Course Format

This course has been designed for independent study. It includes all of the materials you will need to understand the concepts covered in this subject. The materials in this course include:

- Lecture videos from Spring 2011, taught by Prof. Dennis Freeman
- Recitation videos, developed for OCW Scholar by teaching assistant Kendra Pugh
- Course notes
- Software and design labs
- Homework assignments and additional exercises
- Nano-quizzes and exams with solutions

#### Content Development

Leslie Kaelbling

Jacob White

Harold Abelson

Dennis Freeman

Tomás Lozano-Pérez

Isaac Chuang

## Related Content

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.

The subject introduces the principles of ocean surface waves and their interactions with ships, offshore platforms and advanced marine vehicles. Surface wave theory is developed for linear and nonlinear deterministic and random waves excited by the environment, ships, or floating structures.

Following the development of the physics and mathematics of surface waves, several applications from the field of naval architecture and offshore engineering are addressed. They include the ship Kelvin wave pattern and wave resistance, the interaction of surface waves with floating bodies, the seakeeping of ships high-speed vessels and offshore platforms, the evaluation of the drift forces and other nonlinear wave effects responsible for the slow-drift responses of compliant offshore platforms and their mooring systems designed for hydrocarbon recovery from large water depths.

This course was originally offered in Course 13 (Department of Ocean Engineering) as 13.022. In 2005, ocean engineering subjects became part of Course 2 (Department of Mechanical Engineering), and this course was renumbered 2.24.

This course forms an introduction to a selection of mathematical topics that are not covered in traditional mechanical engineering curricula, such as differential geometry, integral geometry, discrete computational geometry, graph theory, optimization techniques, calculus of variations and linear algebra. The topics covered in any particular year depend on the interest of the students and instructor. Emphasis is on basic ideas and on applications in mechanical engineering. This year, the subject focuses on selected topics from linear algebra and the calculus of variations. It is aimed mainly (but not exclusively) at students aiming to study mechanics (solid mechanics, fluid mechanics, energy methods etc.), and the course introduces some of the mathematical tools used in these subjects. Applications are related primarily (but not exclusively) to the microstructures of crystalline solids.

The course material emphasizes mathematical models for predicting distribution and fate of effluents discharged into lakes, reservoirs, rivers, estuaries, and oceans. It also focuses on formulation and structure of models as well as analytical and simple numerical solution techniques. Also discussed are the role of element cycles, such as oxygen, nitrogen, and phosphorus, as water quality indicators; offshore outfalls and diffusion; salinity intrusion in estuaries; and thermal stratification, eutrophication, and sedimentation processes in lakes and reservoirs. This course is a core requirement for the Environmental MEng program.

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