RES.TLL004 STEM Concept Videos  Differential Equations
http://ocw.mit.edu/resources/restll004stemconceptvideosfall2013/videos/differentialequations
20140825T15:51:27+05:00
MIT OpenCourseWare http://ocw.mit.edu
enUS
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 (AttributionNonCommercialShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

Gradient
<h2 class="subhead">Summary</h2> <p>This video leads students through an understanding of how the gradient is used in Fick's first law to describe a relationship between the flux of particles and the concentration of particles. This relationship is explored by modeling the process of diffusion using random walkers. Finally, this law is applied to other realworld scenarios involving solid state diffusion and thermodynamics.</p> <h2 class="subhead">Learning Objectives</h2> <p>After watching this video students should be able to:</p> <ul> <li>Recognize that the gradient vector points in the direction of maximum slope of a scalar function with magnitude equal to that slope.</li> <li>Describe the physicality of Fick’s first law as it applies to concentration gradients.</li> </ul> <p> </p> <p>Funding provided by the Singapore University of Technology and Design (SUTD)</p> <p>Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD</p> <p>MIT © 2012</p>Thumbnail  <a href= http://img.youtube.com/vi/mDvty90jENM/default.jpg>JPG (YouTube)</a><br>Video  download: <a href= http://www.archive.org/download/MITRES.TLL004F13/MITRES_TLL004F13_gradient_intro_300k.mp4>Internet Archive (MP4)</a><br>Video  download: <a href= https://itunes.apple.com/us/itunesu/gradient/id765926614?i=194533716>iTunes U (MP4)</a><br>Video  stream: <a href= http://www.youtube.com/v/mDvty90jENM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BYNCSA)</a><br><br>
http://ocw.mit.edu/resources/restll004stemconceptvideosfall2013/videos/differentialequations/gradient
Teaching and Learning Laboratory (TLL)
Singapore University of Technology and Design (SUTD)
20131230T16:02:35+05:00
enUS
MIT OpenCourseWare http://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 (AttributionNonCommercialShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

Enzyme Kinetics
<h2 class="subhead">Summary</h2> <p>Prof. Krystyn Van Vliet discusses the importance and utility of enzyme kinetics for drug development. Alongside the video, students derive a rate equation (the MichaelisMenten equation) for a simple enzymesubstrate system. Returning to the drug development example, students see that rate equations can help them infer information about reaction mechanisms.</p> <h2 class="subhead">Learning Objectives</h2> <p>After watching this video students will be able to:</p> <ul> <li>Explain how enzymes affect reaction rates.</li> <li>Derive a rate law for a general enzymecatalyzed reaction.</li> </ul><p> </p><p>Funding provided by the Singapore University of Technology and Design (SUTD)</p><p>Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD</p><p>MIT © 2012</p>Thumbnail  <a href= http://img.youtube.com/vi/FXWZr3mscUo/default.jpg>JPG (YouTube)</a><br>Video  download: <a href= http://www.archive.org/download/MITRES.TLL004F13/MITRES_TLL004F13_enzyme_kinetics_intro_300k.mp4>Internet Archive (MP4)</a><br>Video  download: <a href= https://itunes.apple.com/us/itunesu/enzymekinetics/id765926614?i=194533714>iTunes U (MP4)</a><br>Video  stream: <a href= http://www.youtube.com/v/FXWZr3mscUo>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BYNCSA)</a><br><br>
http://ocw.mit.edu/resources/restll004stemconceptvideosfall2013/videos/differentialequations/enzymekinetics
Teaching and Learning Laboratory (TLL)
Singapore University of Technology and Design (SUTD)
20131230T16:02:35+05:00
enUS
MIT OpenCourseWare http://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 (AttributionNonCommercialShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

An Ode to ODEs
<h2 class="subhead">Summary</h2> <p>This video leads students through modeling the regular, nonlinear pendulum with a differential equation. We explore why solutions to a differential equation are an infinite family of functions. We show that to determine a specific solution to this second order differential equation, two initial conditions must be specified. Proof of the need for two initial conditions is shown via use of the Taylor Series.</p> <h2 class="subhead">Learning Objectives</h2> <p>After watching this video students will be able to:</p> <ul> <li>Understand that the physical laws governing a system’s properties can be modeled using differential equations.</li> <li>Explain that the solution to a differential equation is a family of functions.</li> <li>Recognize that specifying initial conditions determines a particular solution function to a differential equation.</li> </ul> <p>Funding provided by the Singapore University of Technology and Design (SUTD)</p> <p>Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD</p> <p>MIT © 2012</p>Keywords: Differential equations, pendulum, pivot point, damped harmonic motion, coordinate system, free body diagram, drag force, damping force, second order ordinary differential equation, Taylor series expansion, initial conditions<br><br>Thumbnail  <a href= http://img.youtube.com/vi/8VlloeKvV8E/default.jpg>JPG (YouTube)</a><br>Video  download: <a href= http://www.archive.org/download/MITRES.TLL004F13/MITRES_TLL004F13_an_ode_to_odes_300k.mp4>Internet Archive (MP4)</a><br>Video  download: <a href= https://itunes.apple.com/us/podcast/anodetoodes/id765926614?i=237394842&mt=2>iTunes U (MP4)</a><br>Video  stream: <a href= http://www.youtube.com/v/8VlloeKvV8E>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BYNCSA)</a><br><br>
http://ocw.mit.edu/resources/restll004stemconceptvideosfall2013/videos/differentialequations/anodetoodes
Teaching and Learning Laboratory (TLL)
Singapore University of Technology and Design (SUTD)
20131230T16:02:35+05:00
enUS
Differential equations
pendulum
pivot point
damped harmonic motion
coordinate system
free body diagram
drag force
damping force
second order ordinary differential equation
Taylor series expansion
initial conditions
MIT OpenCourseWare http://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 (AttributionNonCommercialShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

Contaminant Fate Modeling
<h2 class="subhead">Summary</h2><p>This video combines the concepts of modeling, conservation of mass, and differential equations to estimate the concentration of estrogen in Massachusetts Bay. Students consider what the dominant inputs and outputs may be and see how simplifying assumptions make the differential equation easier to solve.</p><h2 class="subhead">Learning Objectives</h2><p>After watching this video students will be able to:</p><ul><li>Construct a differential equation to estimate the concentration of a chemical in the environment.</li><li>Appreciate how informed estimates can help simplify and solve these differential equations.</li></ul><p>Funding provided by the Singapore University of Technology and Design (SUTD)</p><p>Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD</p><p>MIT © 2012</p>Thumbnail  <a href= http://img.youtube.com/vi/mBJCP3AH2Mk/default.jpg>JPG (YouTube)</a><br>Video  download: <a href= http://www.archive.org/download/MITRES.TLL004F13/MITRES_TLL004F13_contaminant_fate_modeling_300k.mp4>Internet Archive (MP4)</a><br>Video  download: <a href= https://itunes.apple.com/us/itunesu/id765926614>iTunes U (MP4)</a><br>Video  stream: <a href= http://www.youtube.com/v/mBJCP3AH2Mk>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BYNCSA)</a><br><br>
http://ocw.mit.edu/resources/restll004stemconceptvideosfall2013/videos/differentialequations/contaminantfatemodeling
Teaching and Learning Laboratory (TLL)
Singapore University of Technology and Design (SUTD)
20131230T16:02:35+05:00
enUS
MIT OpenCourseWare http://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 (AttributionNonCommercialShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

Curl
<h2 class="subhead">Summary</h2> <p>This video leads students through the physical definition of the curl, and its connection to the mathematical description. A variety of classical fluid flow environments are analyzed for the existence of curl. Finally, the connection between curl and momentum transfer in fluid flow are explored in the context of biological locomotion.</p> <h2 class="subhead">Learning Objectives</h2> <p>After watching this video students will be able to:</p> <ul> <li>Understand curl as a measurement of the magnitude and direction of maximum circulation per unit area.</li> <li>Recognize curl in 2dimensional fluid flows.</li> <li>Describe the relationship between curl and vorticity.</li> <li>Connect vorticity to momentum transfer for a collection of familiar physical phenomena.</li> </ul> <p>Funding provided by the Singapore University of Technology and Design (SUTD)</p> <p>Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD</p> <p>MIT © 2012</p>Thumbnail  <a href= http://img.youtube.com/vi/2pQW0UrkrQY/default.jpg>JPG (YouTube)</a><br>Video  stream: <a href= http://www.youtube.com/v/2pQW0UrkrQY>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BYNCSA)</a><br><br>
http://ocw.mit.edu/resources/restll004stemconceptvideosfall2013/videos/differentialequations/curl
Teaching and Learning Laboratory (TLL)
Singapore University of Technology and Design (SUTD)
20131230T16:02:35+05:00
enUS
MIT OpenCourseWare http://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 (AttributionNonCommercialShareAlike). For further information see http://ocw.mit.edu/terms/index.htm

Divergence
<h2 class="subhead">Summary</h2><p>This video describes how divergence is a fundamental component of a complex modeling problem involving detonation blasts. The divergence of a vector field is defined physically, and the physical description is connected to the mathematical formula. Students analyze a collection of vector fields to determine whether or not they have positive, negative, or zero divergence by analyzing the change in area or volume of a region of tracer particles.</p><h2 class="subhead">Learning Objectives</h2><p>After watching this video students will be able to determine points at which a vector field is divergent.</p><p>Funding provided by the Singapore University of Technology and Design (SUTD)</p><p>Developed by the Teaching and Learning Laboratory (TLL) at MIT for SUTD</p><p>MIT © 2012</p>Thumbnail  <a href= http://img.youtube.com/vi/f0NgEvOEI/default.jpg>JPG (YouTube)</a><br>Video  stream: <a href= http://www.youtube.com/v/f0NgEvOEI>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BYNCSA)</a><br><br>
http://ocw.mit.edu/resources/restll004stemconceptvideosfall2013/videos/differentialequations/divergence
Teaching and Learning Laboratory (TLL)
Singapore University of Technology and Design (SUTD)
20131230T16:02:35+05:00
enUS
MIT OpenCourseWare http://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 (AttributionNonCommercialShareAlike). For further information see http://ocw.mit.edu/terms/index.htm