MIT OpenCourseWare: New Courses in PhysicsNew courses in Physics from MIT OpenCourseWare, provider of free and open MIT course materials.
https://ocw.mit.edu/courses/physics
2019-08-16T20:56:34+05:00MIT OpenCourseWare https://ocw.mit.eduen-USContent 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.htm8.06 Quantum Physics III (MIT)This course is a continuation of 8.05 Quantum Physics II. It introduces some of the important model systems studied in contemporary physics, including two-dimensional electron systems, the fine structure of hydrogen, lasers, and particle scattering.An edX version of this course, 8.06x Applications of Quantum Mechanics, is available starting on February 20, 2019 and running for 19 weeks.
https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii-spring-2018
Spring2018Zwiebach, Barton2019-02-14T15:37:06+05:008.06en-USquantum physicsHamiltonianperturbation theoryperturbation expansionAnharmonic oscillatorhydrogen atomPauli equationtime dependent perturbation theorytime independent perturbation theoryScatteringidentical particlesMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.13-14 Experimental Physics I & II "Junior Lab" (MIT)Junior Lab consists of two undergraduate courses in experimental physics. The course sequence is usually taken by Juniors (hence the name). Officially, the courses are called Experimental Physics I and II and are numbered 8.13 for the first half, given in the fall semester, and 8.14 for the second half, given in the spring. Each term, students do experiments on phenomena whose discoveries led to major advances in physics. In the process, they deepen their understanding of the relations between experiment and theory, mostly in atomic and nuclear physics.
https://ocw.mit.edu/courses/physics/8-13-14-experimental-physics-i-ii-junior-lab-fall-2016-spring-2017
Fall2016Faculty, Lecturers, and Technical Staff, Physics Department2018-11-01T10:24:57+05:008.13-14en-USJunior Labexperimental physicsphotoelectric effectPoisson statisticselectromagnetic pulseFranck-Hertz experimentrelativistic dynamicsnuclear magnetic resonancecosmic-ray muonsRutherford ScatteringJohnson noiseshot noisequantum mechanicsMössbauer spectroscopyDoppler-free laser spectroscopyRaman spectroscopyMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.321 Quantum Theory I (MIT)This is the first semester of a two-semester graduate-level subject on quantum theory, stressing principles. Quantum theory explains the nature and behavior of matter and energy on the atomic and subatomic level. Topics include Fundamental Concepts, Quantum Dynamics, Composite Systems, Symmetries in Quantum Mechanics, and Approximation Methods.
https://ocw.mit.edu/courses/physics/8-321-quantum-theory-i-fall-2017
Fall2017Todadri, Senthil2018-05-21T16:28:44+05:008.321en-USquantum dynamicsquantum mechanicsSchrödingerHeisenbergketsAharanov-Bohm effectquantum entanglementperturbation theorydensity matricesadiabatic approximationMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.03SC Physics III: Vibrations and Waves (MIT)Vibrations and waves are everywhere. If you take any system and disturb it from a stable equilibrium, the resultant motion will be waves and vibrations. Think of a guitar string—pluck the string, and it vibrates. The sound waves generated make their way to our ears, and we hear the string’s sound. Our eyes see what’s happening because they receive the electromagnetic waves of the light reflected from the guitar string, so that we can recognize the beautiful sinusoidal waves on the string. In fact, without vibrations and waves, we could not recognize the universe around us at all!
The amazing thing is that we can describe many fascinating phenomena arising from very different physical systems with mathematics. This course will provide you with the concepts and mathematical tools necessary to understand and explain a broad range of vibrations and waves. You will learn that waves come from many interconnected (coupled) objects when they are vibrating together. We will discuss many of these phenomena, along with related topics, including mechanical vibrations and waves, sound waves, electromagnetic waves, optics, and gravitational waves.
https://ocw.mit.edu/courses/physics/8-03sc-physics-iii-vibrations-and-waves-fall-2016
Fall2016Lee, Yen-Jie2018-04-18T20:40:04+05:008.03SCen-USmechanical vibrationswavessimple harmonic motionsuperpositionforced vibrationsresonancecoupled oscillationsnormal modesvibrations of continuous systemsreflectionrefractionphasegroup velocity. Opticswave solutions to Maxwell's equationspolarizationSnell's LawinterferenceHuygens's principleMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.223 Classical Mechanics II (MIT)This undergraduate course is a broad, theoretical treatment of classical mechanics, useful in its own right for treating complex dynamical problems, but essential to understanding the foundations of quantum mechanics and statistical physics.
https://ocw.mit.edu/courses/physics/8-223-classical-mechanics-ii-january-iap-2017
January IAP2017Evans, Matthew2017-08-09T15:26:36+05:008.223en-USEquations of MotionLagrangian MechanicsConservedQuantitiesOrbitsScattering OscillationsTricky PotentialsHamiltonian MechanicsCanonical EquationsMotion of a Rigid BodyMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.04 Quantum Physics I (MIT)This is the first course in the undergraduate Quantum Physics sequence. It introduces the basic features of quantum mechanics. It covers the experimental basis of quantum physics, introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions.This presentation of 8.04 by Barton Zwiebach (2016) differs somewhat and complements nicely the presentation of Allan Adams (2013). Adams covers a larger set of ideas; Zwiebach tends to go deeper into a smaller set of ideas, offering a systematic and detailed treatment. Adams begins with the subtleties of superpostion, while Zwiebach discusses the surprises of interaction-free measurements. While both courses overlap over a sizable amount of standard material, Adams discussed applications to condensed matter physics, while Zwiebach focused on scattering and resonances. The different perspectives of the instructors make the problem sets in the two courses rather different.
https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2016
Spring2016Zwiebach, Barton2017-07-05T16:15:47+05:008.04en-USquantum physics: photoelectric effectCompton scatteringphotonsFranck-Hertz experimentthe Bohr atomelectron diffractiondeBroglie waveswave-particle duality of matter and lightwave mechanics: Schroedinger's equationwave functionswave packetsprobability amplitudesstationary statesthe Heisenberg uncertainty principlezero-point energiestransmission and reflection at a barrierbarrier penetrationpotential wellssimple harmonic oscillatorSchroedinger's equation in three dimensions: central potentials, and introduction to hydrogenic systems.MIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.01SC Classical Mechanics (MIT)This first course in the physics curriculum introduces classical mechanics. Historically, a set of core concepts—space, time, mass, force, momentum, torque, and angular momentum—were introduced in classical mechanics in order to solve the most famous physics problem, the motion of the planets. The principles of mechanics successfully described many other phenomena encountered in the world. Conservation laws involving energy, momentum and angular momentum provided a second parallel approach to solving many of the same problems. In this course, we will investigate both approaches: Force and conservation laws. Our goal is to develop a conceptual understanding of the core concepts, a familiarity with the experimental verification of our theoretical laws, and an ability to apply the theoretical framework to describe and predict the motions of bodies.
https://ocw.mit.edu/courses/physics/8-01sc-classical-mechanics-fall-2016
Fall2016Chakrabarty, DeeptoDourmashkin, PeterTomasik, MichelleFrebel, AnnaVuletic, Vladan2017-06-02T17:19:25+05:008.01SCen-USclassical mechanicsSpace and timestraight-line kinematicsmotion in a planeforces and equilibriumexperimental basis of Newton's lawsparticle dynamicsuniversal gravitationcollisions and conservation lawswork and potential energyvibrational motionconservative forcesinertial forces and non-inertial framescentral force motionsrigid bodies and rotational dynamicsMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.06 Quantum Physics III (MIT)8.06 is the third course in the three-sequence physics undergraduate Quantum Mechanics curriculum. By the end of this course, you will be able to interpret and analyze a wide range of quantum mechanical systems using both exact analytic techniques and various approximation methods. This course will introduce some of the important model systems studied in contemporary physics, including two-dimensional electron systems, the fine structure of Hydrogen, lasers, and particle scattering.
https://ocw.mit.edu/courses/physics/8-06-quantum-physics-iii-spring-2016
Spring2016Harrow, Aram2016-07-22T22:25:34+05:008.06en-USnatural unitsscales of microscopic phenomenaTime-independent approximation methods: degenerate and non-degenerate perturbation theoryvariational methodBorn-Oppenheimer approximationspin-orbit and relativistic correctionsZeeman and Stark effectsCharged particles in a magnetic fieldLandau levelsinteger quantum hall effectScatteringpartial wavesBorn approximationTime-dependent perturbation theoryMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.821 String Theory and Holographic Duality (MIT)This string theory course focuses on holographic duality (also known as gauge / gravity duality or AdS / CFT) as a novel method of approaching and connecting a range of diverse subjects, including quantum gravity / black holes, QCD at extreme conditions, exotic condensed matter systems, and quantum information.
https://ocw.mit.edu/courses/physics/8-821-string-theory-and-holographic-duality-fall-2014
Fall2014Liu, Hong2016-03-02T20:58:27+05:008.8218.871en-USstring theoryholographic dualityWeinberg-WittenAdS/CFT dualityblack holesHolographic principleWilson loopsEntanglement entropyQuark-gluon plasmasquantum gravityHamilton-JacobiD-branesLarge-N ExpansionLight-Cone GaugeMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.591J Systems Biology (MIT)This course provides an introduction to cellular and population-level systems biology with an emphasis on synthetic biology, modeling of genetic networks, cell-cell interactions, and evolutionary dynamics. Cellular systems include genetic switches and oscillators, network motifs, genetic network evolution, and cellular decision-making. Population-level systems include models of pattern formation, cell-cell communication, and evolutionary systems biology.
https://ocw.mit.edu/courses/physics/8-591j-systems-biology-fall-2014
Fall2014Gore, Jeff2015-07-27T20:48:39+05:008.591J7.81J7.32en-USmolecular systems biologygenetic networkscontrol theorysynthetic genetic switchesbacterial chemotaxisgenetic oscillatorscircadian rhythmscellular systems biologyreaction diffusion equationslocal activationglobal inhibition modelsgradient sensing systemscenter finding networksgeneral pattern formation modelscell-cell communicationquorum sensingMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.09 Classical Mechanics III (MIT)This course covers Lagrangian and Hamiltonian mechanics, systems with constraints, rigid body dynamics, vibrations, central forces, Hamilton-Jacobi theory, action-angle variables, perturbation theory, and continuous systems. It provides an introduction to ideal and viscous fluid mechanics, including turbulence, as well as an introduction to nonlinear dynamics, including chaos.
https://ocw.mit.edu/courses/physics/8-09-classical-mechanics-iii-fall-2014
Fall2014Stewart, Iain2015-05-08T16:56:31+05:008.09en-USLagrangian mechanicsHamiltonian mechanicssystems with constraintsrigid body dynamicsvibrationscentral forcesHamilton-Jacobi theoryaction-angle variablesperturbation theorycontinuous systemsideal fluid mechanicsviscous fluid mechanicsturbulencenonlinear dynamicschaosMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.421 Atomic and Optical Physics I (MIT)This is the first of a two-semester subject sequence that provides the foundations for contemporary research in selected areas of atomic and optical physics. Topics covered include the interaction of radiation with atoms: resonance; absorption, stimulated and spontaneous emission; methods of resonance, dressed atom formalism, masers and lasers, cavity quantum electrodynamics; structure of simple atoms, behavior in very strong fields; fundamental tests: time reversal, parity violations, Bell's inequalities; and experimental methods.
https://ocw.mit.edu/courses/physics/8-421-atomic-and-optical-physics-i-spring-2014
Spring2014Ketterle, Wolfgang2015-03-17T17:29:48+05:008.421en-USatomatomic and optical physicsresonanceresonance frequencyharmonic oscillatoroscillation frequencymagnetic fieldelectric fieldLandau-Zener problemlamb shiftline broadeningcoherenceMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.333 Statistical Mechanics I: Statistical Mechanics of Particles (MIT)Statistical Mechanics is a probabilistic approach to equilibrium properties of large numbers of degrees of freedom. In this two-semester course, basic principles are examined. Topics include: Thermodynamics, probability theory, kinetic theory, classical statistical mechanics, interacting systems, quantum statistical mechanics, and identical particles.
https://ocw.mit.edu/courses/physics/8-333-statistical-mechanics-i-statistical-mechanics-of-particles-fall-2013
Fall2013Kardar, Mehran2014-12-19T22:14:55+05:008.333en-USthermodynamicsentropymehanicsmicrocanonical distributionscanonical distributionsgrand canonical distributionslattice vibrationsideal gasphoton gasquantum statistical mechanicsFermi systemsBose systemscluster expansionsvan der Waal's gasmean-field theoryMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.334 Statistical Mechanics II: Statistical Physics of Fields (MIT)This is the second term in a two-semester course on statistical mechanics. Basic principles are examined in this class, such as the laws of thermodynamics and the concepts of temperature, work, heat, and entropy. Topics from modern statistical mechanics are also explored, including the hydrodynamic limit and classical field theories.
https://ocw.mit.edu/courses/physics/8-334-statistical-mechanics-ii-statistical-physics-of-fields-spring-2014
Spring2014Kardar, Mehran2014-12-19T22:14:44+05:008.334en-USthe hydrodynamic limit and classical field theoriesPhase transitions and broken symmetries: universalitycorrelation functionsand scaling theoryThe renormalization approach to collective phenomenaDynamic critical behaviorRandom systemsMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.422 Atomic and Optical Physics II (MIT)This is the second of a two-semester subject sequence beginning with Atomic and Optical Physics I (8.421) that provides the foundations for contemporary research in selected areas of atomic and optical physics. Topics covered include non-classical states of light–squeezed states; multi-photon processes, Raman scattering; coherence–level crossings, quantum beats, double resonance, superradiance; trapping and cooling-light forces, laser cooling, atom optics, spectroscopy of trapped atoms and ions; atomic interactions–classical collisions, quantum scattering theory, ultracold collisions; and experimental methods.
https://ocw.mit.edu/courses/physics/8-422-atomic-and-optical-physics-ii-spring-2013
Spring2013Ketterle, Wolfgang2014-07-10T10:44:58+05:008.422en-USatomicoptical physicssqueezed statessingle photonCasimir forceoptical Bloch equationsPhoton-atom interactionslight forcesquantum gasesion traps and quantum gatesMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.286 The Early Universe (MIT)The Early Universe provides an introduction to modern cosmology. The first part of the course deals with the classical cosmology, and later part with modern particle physics and its recent impact on cosmology.For more about Professor Guth's work, listen to this interview from WBUR, Boston's National Public Radio news station.
https://ocw.mit.edu/courses/physics/8-286-the-early-universe-fall-2013
Fall2013Guth, Alan2014-07-01T19:13:10+05:008.286en-USspecial relativitybig-bang theoryDoppler effectNewtonian cosmological modelsnon-Euclidean spacesthermal radiationearly history of the universegrand unified theoriesparticle theorybaryogenesisinflationary universe modelevolution of galactic structureMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.04 Quantum Physics I (MIT)This course covers the experimental basis of quantum physics. It introduces wave mechanics, Schrödinger's equation in a single dimension, and Schrödinger's equation in three dimensions.It is the first course in the undergraduate Quantum Physics sequence, followed by 8.05 Quantum Physics II and 8.06 Quantum Physics III.
https://ocw.mit.edu/courses/physics/8-04-quantum-physics-i-spring-2013
Spring2013Adams, AllanEvans, MatthewZwiebach, Barton2014-06-18T18:41:49+05:008.04en-USquantum physics: photoelectric effectCompton scatteringphotonsFranck-Hertz experimentthe Bohr atomelectron diffractiondeBroglie waveswave-particle duality of matter and lightwave mechanics: Schroedinger's equationwave functionswave packetsprobability amplitudesstationary statesthe Heisenberg uncertainty principlezero-point energiestransmission and reflection at a barrierbarrier penetrationpotential wellssimple harmonic oscillatorSchroedinger's equation in three dimensions: central potentials, and introduction to hydrogenic systemsMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.05 Quantum Physics II (MIT)Together, this course and 8.06 Quantum Physics III cover quantum physics with applications drawn from modern physics. Topics covered in this course include the general formalism of quantum mechanics, harmonic oscillator, quantum mechanics in three-dimensions, angular momentum, spin, and addition of angular momentum.
https://ocw.mit.edu/courses/physics/8-05-quantum-physics-ii-fall-2013
Fall2013Zwiebach, Barton2014-06-17T20:00:31+05:008.05en-USquantum physicsquantum mechanicsSchrodinger equationDirac's notationHarmonic oscillatorwave functionsangular momentumeigenvalueseigenstatesspherical harmonicsspin systemsMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.851 Effective Field Theory (MIT)Effective field theory is a fundamental framework to describe physical systems with quantum field theory. Part I of this course covers common tools used in effective theories. Part II is an in depth study of the Soft-Collinear Effective Theory (SCET), an effective theory for hard interactions in collider physics.
https://ocw.mit.edu/courses/physics/8-851-effective-field-theory-spring-2013
Spring2013Stewart, Iain2014-01-13T19:27:27+05:008.851en-USQuarksRelativistic Quantum Field TheoryQuantum Chromodynamics (QCD)The QCD LangrangianAsymptotic FreedomDeep Inelastic ScatteringJets, The QCD VacuumInstantonsthe U(1) ProblemLattice Guage TheoryMIT OpenCourseWare https://ocw.mit.eduContent 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.htm8.044 Statistical Physics I (MIT)This course offers an introduction to probability, statistical mechanics, and thermodynamics. Numerous examples are used to illustrate a wide variety of physical phenomena such as magnetism, polyatomic gases, thermal radiation, electrons in solids, and noise in electronic devices.This course is an elective 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.
https://ocw.mit.edu/courses/physics/8-044-statistical-physics-i-spring-2013
Spring2013Greytak, Thomas2014-01-07T21:52:01+05:008.044en-USprobabilitystatistical mechanicsthermodynamicsrandom variablesjoint and conditional probability densitiesfunctions of a random variablemacroscopic variablesthermodynamic equilibriumfundamental assumption of statistical mechanicsmicrocanonical and canonical ensemblesFirst, second, and third laws of thermodynamicsmagnetismpolyatomic gasesthermal radiationelectrons in solidsnoise in electronic devicesMIT OpenCourseWare https://ocw.mit.eduContent 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