New courses in Biological Engineering from MIT OpenCourseWare, provider of free and open MIT course materials. https://ocw.mit.edu/courses/biological-engineering 2022-02-11T17:21:36+05:00 MIT OpenCourseWare https://ocw.mit.edu en-US Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course covers the fundamental driving forces for transport—chemical gradients, electrical interactions, and fluid flow—as applied to the biology and biophysics of molecules, cells, and tissues. https://ocw.mit.edu/courses/biological-engineering/20-430j-fields-forces-and-flows-in-biological-systems-fall-2015 Fall 2015 Bathe, Mark Grodzinsky, Alan 2016-06-29T19:42:11+05:00 20.430J 2.795J 6.561J 10.539J en-US diffusion molecular diffusion diffusion-reaction conduction convection biological systems fields electrical double layers Maxwell stress tensor physiological systems fluid solid equations of motion case study electrode interfaces transduction random walk Stokes-Einstein Fick's laws reaction Damköhler number MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course provides broad exposure to research in biophysics and physical biology, with emphasis on the critical evaluation of scientific literature. Weekly meetings include in-depth discussion of scientific literature led by various MIT faculty on active research topics. Each session also includes a brief discussion of non-research topics including effective presentation skills, writing papers and fellowship proposals, choosing scientific and technical research topics, time management, and scientific ethics. https://ocw.mit.edu/courses/biological-engineering/20-416j-topics-in-biophysics-and-physical-biology-fall-2014 Fall 2014 Bathe, Mark Gore, Jeff 2016-05-11T11:31:46+05:00 20.416J 7.74J 8.590J en-US 20.416J 20.416 7.74J 7.74 8.590J 8.590 computational biology science research genome chromatin fellowship proposal grad school graduate school nano writing journal article abstract peer review critique manuscript talk presentation ethics cv curriculum vitae MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm Becoming the Next Bill Nye is about using video production techniques to develop your ability to engagingly convey your passions for science, technology, engineering, and / or math. You'll have the opportunity to script and on-screen host 5-minute YouTube science, technology, engineering, and / or math-related shows to inspire youth to consider a future in science. https://ocw.mit.edu/courses/biological-engineering/20-219-becoming-the-next-bill-nye-writing-and-hosting-the-educational-show-january-iap-2015 January IAP 2015 Choe, Elizabeth Goldstein, Jaime Boebel, Chris Zaidan, George Gunn, Joshua Riley, Ceri Kuldell, Natalie 2016-03-01T23:37:51+05:00 20.219 en-US STEM video education entertainment edutainment camera film production host Bill Nye science technology math engineering Hank Green MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course develops and applies scaling laws and the methods of continuum and statistical mechanics to biomechanical phenomena over a range of length scales, from molecular to cellular to tissue or organ level. https://ocw.mit.edu/courses/biological-engineering/20-310j-molecular-cellular-and-tissue-biomechanics-spring-2015 Spring 2015 Kamm, Roger Grodzinsky, Alan 2016-01-15T21:34:48+05:00 20.310J 3.053J 6.024J 2.797J en-US biomechanics molecular mechanics cell mechanics Brownian motion Reynolds numbers mechanochemistry Kramers' model Bell model viscoelasticity poroelasticity optical tweezers extracellular matrix collagen proteoglycan cell membrane cell motility mechanotransduction cancer biological systems molecular biology cell biology cytoskeleton cell biophysics cell migration biomembrane tissue mechanics rheology polymer length scale muscle mechanics experimental methods MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course addresses the scientific basis for the development of new drugs. The first half of the semester begins with an overview of the drug discovery process, followed by fundamental principles of pharmacokinetics, pharmacodynamics, metabolism, and the mechanisms by which drugs cause therapeutic and toxic responses. The second half of the semester applies those principles to case studies and literature discussions of current problems with specific drugs, drug classes, and therapeutic targets. https://ocw.mit.edu/courses/biological-engineering/20-201-mechanisms-of-drug-actions-fall-2013 Fall 2013 Dedon, Peter Tannenbaum, Steven Murcko, Mark Knutson, Charles 2014-06-25T14:06:05+05:00 20.201 en-US drugs medicine pharmaceutical pharmacology toxicology drug actions therapeutics histology pathophysiology drug therapy drug transporters drug metabolism drug toxicity drug development uptake transport case study biochemistry Pharmacokinetics Pharmacogenetics Omeprazole antibiotics Oncology Statins Sarilumab cystic fibrosis MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course focuses on computational and experimental analysis of biological systems across a hierarchy of scales, including genetic, molecular, cellular, and cell population levels. The two central themes of the course are modeling of complex dynamic systems and protein design and engineering. Topics include gene sequence analysis, molecular modeling, metabolic and gene regulation networks, signal transduction pathways and cell populations in tissues. Emphasis is placed on experimental methods, quantitative analysis, and computational modeling. https://ocw.mit.edu/courses/biological-engineering/20-320-analysis-of-biomolecular-and-cellular-systems-fall-2012 Fall 2012 Fraenkel, Ernest White, Forest 2014-05-01T16:48:56+05:00 20.320 en-US biological engineering kinase PyMOL PyRosetta MATLAB Michaelis-Menten bioreactor bromodomain protein-ligand interactions titration analysis fractional separation isothermal titration calorimetry ITC mass spectrometry MS co-immunoprecipitation Co-IP Forster resonance energy transfer FRET primary ligation assay PLA surface plasmon resonance SPR enzyme kinetics kinase engineering competitive inhibition epidermal growth factor receptor mitogen-activated protein kinase MAPK genome editing Imatinib Gleevec Glivec drug delivery kinetics of molecular processes dynamics of molecular processes kinetics of cellular processes dynamics of cellular processes intracellular scale extracellular scale and cell population scale biotechnology applications gene regulation networks nucleic acid hybridization signal transduction pathways cell populations in tissues cell populations in bioreactors experimental methods quantitative analysis computational modeling MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course introduces experimental biochemical and molecular techniques from a quantitative engineering perspective. Experimental design, data analysis, and scientific communication form the underpinnings of this subject. Three discovery-based experimental modules focus on RNA engineering, protein engineering, and cell-biomaterial engineering.This OCW site is based on the source OpenWetWare class Wiki, 20.109(S10): Laboratory Fundamentals of Biological Engineering. https://ocw.mit.edu/courses/biological-engineering/20-109-laboratory-fundamentals-in-biological-engineering-spring-2010 Spring 2010 Stachowiak, Agi Jasanoff, Alan Niles, Jacquin Banuazizi, Atissa Lerner, Neal Sutliff, Linda 2011-01-25T14:54:36+05:00 20.109 en-US biology bioengineering biotechnology RNA engineering protein engineering biomaterial engineering assay lab protocol MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course illustrates how knowledge and principles of biology, biochemistry, and engineering are integrated to create new products for societal benefit. It uses a case study format to examine recently developed products of pharmaceutical and biotechnology industries: how a product evolves from initial idea, through patents, testing, evaluation, production, and marketing. Emphasizes scientific and engineering principles; the responsibility scientists, engineers, and business executives have for the consequences of their technology; and instruction and practice in written and oral communication. The topic focus of this class will vary from year to year. This version looks at inflammation underlying many diseases, specifically its role in cancer, diabetes, and cardiovascular disease. https://ocw.mit.edu/courses/biological-engineering/20-380j-biological-engineering-design-spring-2010 Spring 2010 Essigmann, John Irvine, Darrell White, Forest Banuazizi, Atissa Breindel, Harlan Poe, Mya 2011-01-12T15:45:01+05:00 20.380J 5.22J en-US inflammation biomedical engineering cancer diabetes obesity cardiovascular disease biomedical entrepreneurship biomedical startup MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course covers the principles of materials science and cell biology underlying the design of medical implants, artificial organs, and matrices for tissue engineering. Methods for biomaterials surface characterization and analysis of protein adsorption on biomaterials. Molecular and cellular interactions with biomaterials are analyzed in terms of unit cell processes, such as matrix synthesis, degradation, and contraction. Mechanisms underlying wound healing and tissue remodeling following implantation in various organs. Tissue and organ regeneration. Design of implants and prostheses based on control of biomaterials-tissue interactions. Comparative analysis of intact, biodegradable, and bioreplaceable implants by reference to case studies. Criteria for restoration of physiological function for tissues and organs. https://ocw.mit.edu/courses/biological-engineering/20-441j-biomaterials-tissue-interactions-fall-2009 Fall 2009 Yannas, Ioannis Spector, Myron 2010-06-29T18:41:52+05:00 20.441J 2.79J 3.96J HST.522J en-US 20.441J 20.441 2.79J 2.79 3.96J 3.96 HST.522J HST.522 medical implants tissue engineering unit cell process wound healing joint replacement extracellular matrix biocompatibility MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This class is a project-based introduction to the engineering of synthetic biological systems. Throughout the term, students develop projects that are responsive to real-world problems of their choosing, and whose solutions depend on biological technologies. Lectures, discussions, and studio exercises will introduce (1) components and control of prokaryotic and eukaryotic behavior, (2) DNA synthesis, standards, and abstraction in biological engineering, and (3) issues of human practice, including biological safety; security; ownership, sharing, and innovation; and ethics. Enrollment preference is given to freshmen. This subject was originally developed and first taught in Spring 2008 by Drew Endy and Natalie Kuldell. Many of Drew's materials are used in this Spring 2009 version, and are included with his permission. This OCW Web site is based on the OpenWetWare class Wiki, found at OpenWetWare: 20.020 (S09) https://ocw.mit.edu/courses/biological-engineering/20-020-introduction-to-biological-engineering-design-spring-2009 Spring 2009 Kuldell, Natalie Endy, Andrew 2009-12-22T12:36:40+05:00 20.020 en-US biology chemistry synthetic biology project biotech genetic engineering GMO ethics biomedical ethics genetics recombinant DNA DNA gene sequencing gene synthesis biohacking computational biology iGEM BioBrick systems biology MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course teaches the design of contemporary information systems for biological and medical data. Examples are chosen from biology and medicine to illustrate complete life cycle information systems, beginning with data acquisition, following to data storage and finally to retrieval and analysis. Design of appropriate databases, client-server strategies, data interchange protocols, and computational modeling architectures. Students are expected to have some familiarity with scientific application software and a basic understanding of at least one contemporary programming language (e.g. C, C++, Java, Lisp, Perl, Python). A major term project is required of all students. This subject is open to motivated seniors having a strong interest in biomedical engineering and information system design with the ability to carry out a significant independent project. This course was offered as part of the Singapore-MIT Alliance (SMA) program as course number SMA 5304. https://ocw.mit.edu/courses/biological-engineering/20-453j-biomedical-information-technology-fall-2008 Fall 2008 Dewey Jr., C. Forbes Yu, Hanry Bhowmick, Sourav Saha 2009-06-24T14:38:44+05:00 20.453J 2.771J HST.958J en-US 20.453J 20.453 2.771J 2.771 HST.958J HST.958 imaging medical imaging metadata molecular biology medical records DICOM RDF OWL SPARQL SBML CellML semantic web BioHaystack database schema ExperiBase genomics proteomics bioinformatics computational biology clinical decision support clinical trial microarray gel electrophoresis diagnosis pathway modeling XML SQL relational database biological data ontologies drug development drug discovery drug target pharmaceutical gene sequencing MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course introduces experimental biochemical and molecular techniques from a quantitative engineering perspective. Experimental design, rigorous data analysis, and scientific communication form the underpinnings of this subject. Three discovery-based experimental modules focus on genome engineering, expression engineering, and biomaterial engineering.This OCW site is based on the source OpenWetWare class Wiki, found at 20.109(F07): Laboratory Fundamentals of Biological Engineering. https://ocw.mit.edu/courses/biological-engineering/20-109-laboratory-fundamentals-in-biological-engineering-fall-2007 Fall 2007 Endy, Drew Kuldell, Natalie Lerner, Neal Stachowiak, Agi Belcher, Angela M. Banuazizi, Atissa 2008-07-23T20:29:38+05:00 20.109 en-US biological engineering biology bioengineering DNA PCR RNA polymerase chain reaction systems engineering DNA engineering protein engineering bio-material engineering restriction map lipofection screening library bacterial photography device characterization biological parts openwetware MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course introduces the basic driving forces for electric current, fluid flow, and mass transport, plus their application to a variety of biological systems. Basic mathematical and engineering tools will be introduced, in the context of biology and physiology. Various electrokinetic phenomena are also considered as an example of coupled nature of chemical-electro-mechanical driving forces. Applications include transport in biological tissues and across membranes, manipulation of cells and biomolecules, and microfluidics. https://ocw.mit.edu/courses/biological-engineering/20-330j-fields-forces-and-flows-in-biological-systems-spring-2007 Spring 2007 Han, Jongyoon Manalis, Scott 2007-10-25T04:52:44+05:00 20.330J 2.793J 6.023J en-US hydrodynamic flow electroosmosis diffusion electrophoresis reaction membrane cell biomolecule microfluidics ion transport electrokinetics Debye layer Zeta potential inviscid flow viscous flow tissue organ biology molecular biology Maxwell's equations electro-quasistatics Van der Waals bioMEMS MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course covers introductory microbiology from a systems perspective, considering microbial diversity, population dynamics, and genomics. Emphasis is placed on the delicate balance between microbes and humans, and the changes that result in the emergence of infectious diseases and antimicrobial resistance. The case study approach covers such topics as vaccines, toxins, biodefense, and infections including Legionnaire’s disease, tuberculosis, Helicobacter pylori, and plague. https://ocw.mit.edu/courses/biological-engineering/20-106j-systems-microbiology-fall-2006 Fall 2006 Schauer, David DeLong, Edward 2007-10-25T04:51:49+05:00 20.106J 1.084J en-US microbes microbiology systems perspective early earth microbial evolution prokaryote eukaryote archaea bacteria immunology epidemiology MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm 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. https://ocw.mit.edu/courses/biological-engineering/20-181-computation-for-biological-engineers-fall-2006 Fall 2006 Alm, Eric Endy, Andrew 2007-05-11T05:21:15+05:00 20.181 en-US Phylogenetic Inference Molecular Modeling Protein Design Discrete Reaction Event Network Modeling Python genetics DNA sequence genomics gene sequencing UPGMA Newick notation parsimony downpass uppass jukes-cantor invertase genetic memory MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course covers sensing and measurement for quantitative molecular/cell/tissue analysis, in terms of genetic, biochemical, and biophysical properties. Methods include light and fluorescence microscopies; electro-mechanical probes such as atomic force microscopy, laser and magnetic traps, and MEMS devices; and the application of statistics, probability and noise analysis to experimental data. Enrollment preference is given to juniors and seniors. https://ocw.mit.edu/courses/biological-engineering/20-309-biological-engineering-ii-instrumentation-and-measurement-fall-2006 Fall 2006 Shusteff, Maxim So, Peter Manalis, Scott 2007-04-27T05:55:18+05:00 20.309 2.673J 20.409J en-US DNA analysis Fourier analysis FFT DNA melting electronics microscopy microscope probes biology atomic force microscope AFM scanning probe microscope image processing MATLAB convolution optoelectronics rheology fluorescence noise detector optics diffraction optical trap 3D 3-D three-dimensional imaging visualization MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This subject describes and illustrates computational approaches to solving problems in systems biology. A series of case-studies will be explored that demonstrate how an effective match between the statement of a biological problem and the selection of an appropriate algorithm or computational technique can lead to fundamental advances. The subject will cover several discrete and numerical algorithms used in simulation, feature extraction, and optimization for molecular, network, and systems models in biology. https://ocw.mit.edu/courses/biological-engineering/20-482j-foundations-of-algorithms-and-computational-techniques-in-systems-biology-spring-2006 Spring 2006 Tidor, Bruce White, Jacob 2007-01-05T07:22:06+05:00 20.482J 6.581J en-US systems biology algorithms computational techniques protein modeling discrete conformational search molecular dynamics electrostatics network models deconvolution nonlinear dynamics 20.482J 20.482 6.581J 6.581 MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm In this course problems from biological engineering are used to develop structured computer programming skills and explore the theory and practice of complex systems design and construction. The official course Web site can be viewed at: BE.180 Biological Engineering Programming. https://ocw.mit.edu/courses/biological-engineering/20-180-biological-engineering-programming-spring-2006 Spring 2006 Endy, Andrew 2006-11-06T18:30:58+05:00 20.180 en-US biological engineering problems structured computer programming skills theory and practice of complex systems design theory and design of complex systems construction MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This course covers the 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, vaccines, and cell-guiding surfaces. https://ocw.mit.edu/courses/biological-engineering/20-462j-molecular-principles-of-biomaterials-spring-2006 Spring 2006 Irvine, Darrell 2006-11-02T21:14:22+05:00 20.462J 3.962J en-US biomaterials biomaterial engineering biotechnology cell-guiding surface molecular biomaterials drug release polymers pulsatile release polymerization polyer erosion tissue engineering hydrogels adhesion migration drug diffusion molecular switches molecular motors nanoparticles microparticles vaccines drug targeting micro carriers nano carriers intracellular drug delivery 20.462J 20.462 3.962J 3.962 MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm This seminar-format course provides an in-depth presentation and discussion of how engineering and biological approaches can be combined to solve problems in science and technology, emphasizing integration of biological information and methodologies with engineering analysis, synthesis, and design. Emphasis is placed on molecular mechanisms underlying cellular processes, including signal transduction, gene expression networks, and functional responses. https://ocw.mit.edu/courses/biological-engineering/20-400j-perspectives-in-biological-engineering-spring-2006 Spring 2006 Lauffenburger, Douglas Dedon, Peter 2006-11-02T21:08:23+05:00 20.400J 7.548J en-US integration of biological information and methodologies engineering analysis synthesis design molecular mechanisms underlying cellular processes signal transduction gene expression networks functional responses 20.400J 20.400 7.548J 7.548 MIT OpenCourseWare https://ocw.mit.edu Content within individual OCW courses is (c) by the individual authors unless otherwise noted. MIT OpenCourseWare materials are licensed by the Massachusetts Institute of Technology under a Creative Commons License (Attribution-NonCommercial-ShareAlike). For further information see https://ocw.mit.edu/terms/index.htm