http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation 2013-01-12T07:15:55+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> Definition of derivative; the derivative of x to the n where n is an integer; derivatives of sums, differences, products, and quotients.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-1-derivatives-of-some-simple-functions/MITRES18_006F10_26_0201_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-1-derivatives-of-some-simple-functions/MITRES18_006F10_26_0201_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-1-derivatives-of-some-simple-functions/2_1.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0201_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-1-derivatives/id408737555?i=93802652>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/xlamQGapfbY>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-1-derivatives-of-some-simple-functions Gross, Herbert 2010-12-08T09:47:41+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> Approximating delta y by f(x) delta x; discussion of that difference between delta y and f'(x) delta x; introduction to the chain rule.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-2-approximations-and-infinitesimals/MITRES18_006F10_26_0202_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-2-approximations-and-infinitesimals/MITRES18_006F10_26_0202_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-2-approximations-and-infinitesimals/2_2.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0202_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-2-approximations/id408737555?i=93802649>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Fe9DPXvt2ps>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-2-approximations-and-infinitesimals Gross, Herbert 2010-12-08T09:47:41+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> Composition of functions; a graphical interpretation; applications to parametric equations; using the chain rule to extend the concept of finding derivatives.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-3-composite-functions-and-the-chain-rule/MITRES18_006F10_26_0203_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-3-composite-functions-and-the-chain-rule/MITRES18_006F10_26_0203_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-3-composite-functions-and-the-chain-rule/2_3.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0203_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-3-composite/id408737555?i=93802638>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/w_JWcGLiifU>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-3-composite-functions-and-the-chain-rule Gross, Herbert 2010-12-08T09:47:41+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> The concept of an inverse function; differentiation of an inverse function; when is a function invertible?</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-4-differentiation-of-inverse-functions/MITRES18_006F10_26_0204_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-4-differentiation-of-inverse-functions/MITRES18_006F10_26_0204_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-4-differentiation-of-inverse-functions/2_4.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0204_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-4-differentiation/id408737555?i=93802632>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/MNhkoylpyNA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-4-differentiation-of-inverse-functions Gross, Herbert 2010-12-08T09:47:41+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> Finding the derivative when the functional relationship is implied; application to the case of x to the n where n is a rational number; the use of implicit differentiation in the study of related rates.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-5-implicit-differentiation-1/MITRES18_006F10_26_0205_300k-mp4.pdf>PDF (English - US)</a><br>Thumbnail - <a href= http://img.youtube.com/vi/lLmt2UPPuY4/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0205_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-5-implicit/id408737555?i=94940081>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/lLmt2UPPuY4>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-5-implicit-differentiation-1 Gross, Herbert 2010-12-08T09:47:41+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 class="instruction"><span style="font-family: Verdana, Arial, Helvetica, sans-serif; font-size: 11px; color: rgb(0, 0, 0); " class="Apple-style-span"><strong>Topics covered:</strong> Physical interpretation of continuity; the definition of continuity in terms of limits; a geometric interpretation of continuity; analytic consequences.</span></p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-6-continuity/MITRES18_006F10_26_0206_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-6-continuity/MITRES18_006F10_26_0206_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-6-continuity/2_6.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0206_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-6-continuity/id408737555?i=93802641>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/y4EcXTVqFb4>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-6-continuity Gross, Herbert 2010-12-08T09:47:41+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> Basic pre-calculus review; even and odd functions and other symmetries; the role of the first and second derivatives in curve plotting; stationary points; inflections.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-7-curve-plotting/MITRES18_006F10_26_0207_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-7-curve-plotting/MITRES18_006F10_26_0207_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-7-curve-plotting/2_7.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0207_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-7-curve-plotting/id408737555?i=93802653>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/mKMzFKgBluM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-7-curve-plotting Gross, Herbert 2010-12-08T09:47:41+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> High and low points of a curve; techniques for finding them; applications to finding maxima and minima of functions; physical applications.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-8-maxima-and-minima/MITRES18_006F10_26_0208_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-8-maxima-and-minima/MITRES18_006F10_26_0208_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-8-maxima-and-minima/2_8.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0208_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-8-maxima-minima/id408737555?i=93802635>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/ehDAxjFK1jU>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-8-maxima-and-minima Gross, Herbert 2010-12-08T09:47:41+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> Statement of Rolle's Theorem; a geometric interpretation; some cautions; the Mean Value Theorem; consequences of the Mean Value Theorem.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-9-rolles-theorem-and-its-consequences/MITRES18_006F10_26_0209_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-9-rolles-theorem-and-its-consequences/MITRES18_006F10_26_0209_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-9-rolles-theorem-and-its-consequences/2_9.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0209_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-9-rolles-theorem/id408737555?i=93802643>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/GqVQTRb-QoA>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-9-rolles-theorem-and-its-consequences Gross, Herbert 2010-12-08T09:47:41+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> The &quot;opposite&quot; of differentiation; trying to find f(x) knowing f'(x); some examples; some formulas; notation.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-10-inverse-differentiation/MITRES18_006F10_26_0210_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-10-inverse-differentiation/MITRES18_006F10_26_0210_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-10-inverse-differentiation/2_10.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0210_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-10-inverse/id408737555?i=93802636>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/-S5GwNe0xXg>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-10-inverse-differentiation Gross, Herbert 2010-12-08T09:47:41+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> The meaning of the definite integral as g(b) - g(a) where g'(x) = f(x); some applications.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-11-the-definite-indefinite-integral/MITRES18_006F10_26_0211_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-11-the-definite-indefinite-integral/MITRES18_006F10_26_0211_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-11-the-definite-indefinite-integral/2_11.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0211_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-ii-lecture-11-the-definite/id408737555?i=93802631>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/IVVwFEnmFUk>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-ii-differentiation/lecture-11-the-definite-indefinite-integral Gross, Herbert 2010-12-08T09:47:41+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