This section contains video lectures, available as streaming or downloadable media. http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures 2013-04-02T15:52:01+05:00 MIT OpenCourseWare http://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 http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Dot product</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L01.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-1-dot-product/ocw-18_02-f07-lec01_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-1-dot-product/01.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec01_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1875292263?i=1705913266>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/PxCxlsl_YwY>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-1-dot-product Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Determinants; cross product</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L02.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-2-determinants/ocw-18_02-f07-lec02_220ka.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-2-determinants/02.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec02_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1874802054?i=1123033177>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/9FLItlbBUPY>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-2-determinants Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Matrices; inverse matrices</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L03.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-3-matrices/ocw-18_02-f07-lec03_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-3-matrices/03.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec03_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1887552893?i=1528170350>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/bHdzkFrgRcA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-3-matrices Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Square systems; equations of planes</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L04.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-4-square-systems/ocw-18_02-f07-lec04_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-4-square-systems/04.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec04_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1887325499?i=1178401505>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/YBajUR3EFSM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-4-square-systems Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Parametric equations for lines and curves</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L05.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-5-parametric-equations/ocw-18_02-f07-lec05_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-5-parametric-equations/05.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec05_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1887520745?i=1323389964>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/57jzPlxf4fk>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-5-parametric-equations Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Velocity, acceleration - Kepler's second law</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L06.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-6-keplers-second-law/ocw-18_02-f07-lec06_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-6-keplers-second-law/06.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec06_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1875292447?i=1830841834>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/0D4BbCa4gHo>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-6-keplers-second-law Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Review</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L07.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-7-exam-review/ocw-18_02-f07-lec07_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-7-exam-review/07.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec07_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1886786087?i=1409180658>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/U1EcnfTKXJ0>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-7-exam-review Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Level curves; partial derivatives; tangent plane approximation</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L08.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-8-partial-derivatives/ocw-18_02-f07-lec08_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-8-partial-derivatives/08.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec08_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1887488060?i=1371807841>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/dK3NEf13nPc>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-8-partial-derivatives Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Max-min problems; least squares</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L09.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-9-max-min-and-least-squares/ocw-18_02-f07-lec09_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-9-max-min-and-least-squares/09.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec09_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890156870?i=1481767230>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/UYe98CcxPbs>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-9-max-min-and-least-squares Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Second derivative test; boundaries and infinity</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L10.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-10-second-derivative-test/ocw-18_02-f07-lec10_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-10-second-derivative-test/10.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec10_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890025857?i=1868817660>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/3_goGnJm5sA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-10-second-derivative-test Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Differentials; chain rule</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L11.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-11-chain-rule/ocw-18_02-f07-lec11_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-11-chain-rule/11.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec11_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890451787?i=1447411100>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/7eZVshlT33Q>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-11-chain-rule Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Gradient; directional derivative; tangent plane</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L12.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-12-gradient/ocw-18_02-f07-lec12_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-12-gradient/12.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec12_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890156895?i=2082648719>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/2XraaWefBd8>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-12-gradient Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Lagrange multipliers</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L13.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-13-lagrange-multipliers/ocw-18_02-f07-lec13_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-13-lagrange-multipliers/13.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec13_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890533802?i=1815613202>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/15HVevXRsBA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-13-lagrange-multipliers Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Non-independent variables</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L14.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-14-non-independent-variables/ocw-18_02-f07-lec14_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-14-non-independent-variables/14.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec14_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890304425?i=1649654253>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/23xbkrpQuAo>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-14-non-independent-variables Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Partial differential equations; review</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L15.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-15-partial-differential-equations/ocw-18_02-f07-lec15_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-15-partial-differential-equations/15.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec15_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890435488?i=1273284759>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/ChiM2-MV-qM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-15-partial-differential-equations Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Double integrals</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L16.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-16-double-integrals/ocw-18_02-f07-lec16_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-16-double-integrals/16.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec16_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1889747527?i=1336500957>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/YP_B0AapU0c>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-16-double-integrals Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Double integrals in polar coordinates; applications</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L17.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-17-polar-coordinates/ocw-18_02-f07-lec17_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-17-polar-coordinates/17.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec17_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890451874?i=1595873686>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/60e4hdCi1D4>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-17-polar-coordinates Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Change of variables</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L18.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-18-change-of-variables/ocw-18_02-f07-lec18_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-18-change-of-variables/18.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec18_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1889747413?i=1357061800>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/UZb9hZIAvL4>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-18-change-of-variables Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Vector fields and line integrals in the plane</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L19.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-19-vector-fields/ocw-18_02-f07-lec19_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-19-vector-fields/19.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec19_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1889731080?i=1135588735>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/xrypSZU8cBE>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-19-vector-fields Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Path independence and conservative fields</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L20.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-20-path-independence/ocw-18_02-f07-lec20_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-20-path-independence/20.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec20_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890533924?i=1253362723>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/o7UCBjGsRTE>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-20-path-independence Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Gradient fields and potential functions</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L21.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-21-gradient-fields/ocw-18_02-f07-lec21_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-21-gradient-fields/21.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec21_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890583126?i=1843648467>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/z5TPjZrsp2k>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-21-gradient-fields Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Green's theorem</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L22.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-22-greens-theorem/ocw-18_02-f07-lec22_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-22-greens-theorem/22.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec22_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890288226?i=1301649219>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/tYdoS0tkAHA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-22-greens-theorem Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Flux; normal form of Green's theorem</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L23.pdf>PDF (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-23-flux/23.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec23_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890157179?i=1699786815>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/_CdoRiNSrqI>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-23-flux Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Simply connected regions; review</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L24.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-24-simply-connected-regions/ocw-18_02-f07-lec24_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-24-simply-connected-regions/24.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec24_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890173529?i=1429611777>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/PnPIqh7Frlw>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-24-simply-connected-regions Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Triple integrals in rectangular and cylindrical coordinates</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L25.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-25-triple-integrals/ocw-18_02-f07-lec25_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-25-triple-integrals/25.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec25_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890042483?i=1682317276>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/44R5HgbrUmc>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-25-triple-integrals Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Spherical coordinates; surface area</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L26.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-26-spherical-coordinates/ocw-18_02-f07-lec26_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-26-spherical-coordinates/26.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec26_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890419420?i=1436342157>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/RMBGQtwkoyU>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-26-spherical-coordinates Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Vector fields in 3D; surface integrals and flux</p><p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L27.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-27-vector-fields-in-3d/ocw-18_02-f07-lec27_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-27-vector-fields-in-3d/27.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec27_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890042543?i=1461542297>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/phk05iSMezA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-27-vector-fields-in-3d Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Divergence theorem</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L28.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-28-divergence-theorem/ocw-18_02-f07-lec28_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-28-divergence-theorem/28.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec28_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890616082?i=1833066266>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/WfEQabCGAqI>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-28-divergence-theorem Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Divergence theorem (cont.): applications and proof</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L29.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-29-divergence-theorem-cont/ocw-18_02-f07-lec29_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-29-divergence-theorem-cont/29.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec29_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890435881?i=1276544377>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/wu8kXZSAp20>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-29-divergence-theorem-cont Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Line integrals in space, curl, exactness and potentials</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L30.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-30-line-integrals/ocw-18_02-f07-lec30_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-30-line-integrals/30.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec30_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890534511?i=1596953820>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/seO7-TwXH_I>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-30-line-integrals Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Stokes' theorem</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L31.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-31-stokes-theorem/ocw-18_02-f07-lec31_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-31-stokes-theorem/31.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec31_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890763808?i=1240964550>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/tzoYhe3H5dM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-31-stokes-theorem Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Stokes' theorem (cont.); review</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L32.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-32-stokes-theorem-cont/ocw-18_02-f07-lec32_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-32-stokes-theorem-cont/32.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec32_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890157878?i=1199395900>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/sr7kCpzAuYw>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-32-stokes-theorem-cont Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Topological considerations - Maxwell's equations</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L33.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-33-maxwells-equations/ocw-18_02-f07-lec33_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-33-maxwells-equations/33.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec33_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890420127?i=1342537117>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/BChhAS1sFvA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-33-maxwells-equations Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Final review</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L34.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-34-final-review/ocw-18_02-f07-lec34_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-34-final-review/34.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec34_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890174426?i=1832321151>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/ZwpwmGP5ITM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-34-final-review Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm <p><strong>Topics covered:</strong> Final review (cont.)</p> <p><strong>Instructor:</strong> Prof. Denis Auroux</p>Transcript: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/18_022007L35.pdf>PDF (English - US)</a><br>Subtitles: <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-35-final-review-cont/ocw-18_02-f07-lec35_220k.srt>SRT (English - US)</a><br>Thumbnail - <a href= /courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-35-final-review-cont/35.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MIT18.02F07/ocw-18_02-f07-lec35_300k_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://deimos3.apple.com/WebObjects/Core.woa/Browse/mit.edu.1885187900.01885187905.1890305740?i=1509383478>iTunes U (MP4)</a><br>Video - stream: <a href= http://videolectures.net/mit1802f07_multivariable_calculus/>VideoLectures.net </a><br>Video - stream: <a href= http://www.youtube.com/v/24v9onS9Kcg>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/courses/mathematics/18-02-multivariable-calculus-fall-2007/video-lectures/lecture-35-final-review-cont Auroux, Denis 2008-06-13T12:02:35+05:00 en-US 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 (Attribution-NonCommercial-ShareAlike). For further information see http://ocw.mit.edu/terms/index.htm