http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series 2013-01-12T07:16:03+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> Discussion of how infinity differs from &quot;very large&quot;; some sublte and not-so-subtle consequences of the difference; the case against intuition; motivating infinite series in terms of finding area as a limit.</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-vii-infinite-series/lecture-1-many-versus-infinite/MITRES18_006F10_26_0701_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-1-many-versus-infinite/MITRES18_006F10_26_0701_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-1-many-versus-infinite/7_1.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0701_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-vii-lecture-1-many-versus/id408737555?i=93805826>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/iWphmEIO-1E>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-vii-infinite-series/lecture-1-many-versus-infinite 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 special case wherein each term in the series is non-negative; the concept of convergence; the comparision test; the ratio test; the integral test.</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-vii-infinite-series/lecture-2-positive-series/MITRES18_006F10_26_0702_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-2-positive-series/MITRES18_006F10_26_0702_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-2-positive-series/7_2.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0702_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-vii-lecture-2-positive/id408737555?i=93805822>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/AaucguWxpqU>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-vii-infinite-series/lecture-2-positive-series 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> Non-absolute convergence; conditional and absolute convergence; a series converging when each of its negative terms is replaced by the absolute value of that term; geometric interpretation.</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-vii-infinite-series/lecture-3-absolute-convergence/MITRES18_006F10_26_0703_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-3-absolute-convergence/MITRES18_006F10_26_0703_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-3-absolute-convergence/7_3.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0703_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-vii-lecture-3-absolute/id408737555?i=93805820>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/jUkuRYDU4jA>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-vii-infinite-series/lecture-3-absolute-convergence 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> Using an nth degree polynomial to approximate a function f(x); how to choose the coefficients; power series; Taylor's Remainder Theorem; expressing functions in terms of power series.</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-vii-infinite-series/lecture-4-polynomial-approximations/MITRES18_006F10_26_0704_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-4-polynomial-approximations/MITRES18_006F10_26_0704_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-4-polynomial-approximations/7_4.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0704_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-vii-lecture-4-polynomial/id408737555?i=93805819>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/XaxjVRXonPg>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-vii-infinite-series/lecture-4-polynomial-approximations 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> Pointwise convergence versus uniform convergence; some important consequences of uniform convergence; applications of uniform convergence to the study of power series.</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-vii-infinite-series/lecture-5-uniform-convergence/MITRES18_006F10_26_0705_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-5-uniform-convergence/MITRES18_006F10_26_0705_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-5-uniform-convergence/7_5.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0705_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-vii-lecture-5-uniform/id408737555?i=93805824>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/iM4DRgFqPso>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-vii-infinite-series/lecture-5-uniform-convergence 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> Weirstrass M-test; using power series to evaluate definite integrals when we do not know the anti-derivative of the integrand.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p><p>Ready to move on to Calculus II: Functions of Several Variables? Professor Gross has posted links to the next videos in the series on his <a href="http://www.adjectivenounmath.com/index.html">Mathematics As A Second Language</a> website.</p>Transcript: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-6-uniform-convergence-of-power-series/MITRES18_006F10_26_0706_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-6-uniform-convergence-of-power-series/MITRES18_006F10_26_0706_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-vii-infinite-series/lecture-6-uniform-convergence-of-power-series/7_6.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0706_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-vii-lecture-6-uniform/id408737555?i=93805821>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/3Dz59nKUafo>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-vii-infinite-series/lecture-6-uniform-convergence-of-power-series 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