http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral 2013-01-12T07:15:59+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> Axiomatic approach to area; area approximations by upper and lower bounds; the method of exhaustion; using limits to find areas of nonrectilinear regions; piecewise continuity; trapezoidal approximations.</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-iv-the-definite-integral/lecture-1-the-definite-integral/MITRES18_006F10_26_0401_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral/lecture-1-the-definite-integral/MITRES18_006F10_26_0401_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral/lecture-1-the-definite-integral/4_1.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0401_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-iv-lecture-1-the-definite/id408737555?i=93802647>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/EeLD_40wDoU>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-iv-the-definite-integral/lecture-1-the-definite-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 <p><strong>Topics covered:</strong> First Fundamental Theorem of Integral Calculus; some applications; Second Fundamental Theorem of Integral Calculus; some applications; significance of the two theorems.</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-iv-the-definite-integral/lecture-2-marriage-of-differential-and-integral-calculus/MITRES18_006F10_26_0402_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral/lecture-2-marriage-of-differential-and-integral-calculus/MITRES18_006F10_26_0402_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral/lecture-2-marriage-of-differential-and-integral-calculus/4_2.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0402_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-iv-lecture-2-marriage/id408737555?i=93802650>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/8-7daeS7hYY>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-iv-the-definite-integral/lecture-2-marriage-of-differential-and-integral-calculus 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> Extending the axioms of area to volume; some applications; the method of cylindrical shells.</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-iv-the-definite-integral/lecture-3-three-dimensional-area/MITRES18_006F10_26_0403_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral/lecture-3-three-dimensional-area/MITRES18_006F10_26_0403_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral/lecture-3-three-dimensional-area/4_3.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0403_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-iv-lecture-3-three-dimensional/id408737555?i=93802645>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/7GZTjIxm32I>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-iv-the-definite-integral/lecture-3-three-dimensional-area 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 main difference between arc-length and either area or volume; the limit definition of arc-length; approximating errors and their magnitude when we use infinite sums.</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-iv-the-definite-integral/lecture-4-one-dimensional-area/MITRES18_006F10_26_0404_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral/lecture-4-one-dimensional-area/MITRES18_006F10_26_0404_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-iv-the-definite-integral/lecture-4-one-dimensional-area/4_4.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0404_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-iv-lecture-4-one-dimensional/id408737555?i=93802633>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/A1bPRw9VBQo>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-iv-the-definite-integral/lecture-4-one-dimensional-area 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