http://ocw.mit.edu/resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits 2013-01-12T07:15:52+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> Cartesian coordinates; curves as sets of points; graphs of functions; equations of straight lines; simultaneous linear equations.</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-i-sets-functions-and-limits/lecture-1-analytic-geometry/MITRES18_006F10_26_0101_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-1-analytic-geometry/MITRES18_006F10_26_0101_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-1-analytic-geometry/1_1.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0101_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-i-lecture-1-analytic/id408737555?i=93802646>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/rXOGLlKuvzU>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-i-sets-functions-and-limits/lecture-1-analytic-geometry 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> Notations; concepts of onto and one-to-one; the arithmetic of functions of a real variable; intervals and deleted neighborhoods; absolute values; composition of functions</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-i-sets-functions-and-limits/lecture-2-functions/MITRES18_006F10_26_0102_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-2-functions/MITRES18_006F10_26_0102_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-2-functions/1_2.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0102_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-i-lecture-2-functions/id408737555?i=93802634>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/dNyLGmiYQY0>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-i-sets-functions-and-limits/lecture-2-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> The concept of an inverse function; graphical interpretation; single-valued and multivalued functions; branches of functions.</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-i-sets-functions-and-limits/lecture-3-inverse-functions/MITRES18_006F10_26_0103_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-3-inverse-functions/MITRES18_006F10_26_0103_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-3-inverse-functions/1_3.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0103_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-i-lecture-3-inverse-functions/id408737555?i=93802637>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/elputTS7tAA>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-i-sets-functions-and-limits/lecture-3-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> Instantaneous speed as an outgrowth of average speed; definition of limi; instantaneous speed as a limit; the formal definition of limit and some consequences.</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-i-sets-functions-and-limits/lecture-4-derivatives-and-limits/MITRES18_006F10_26_0104_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-4-derivatives-and-limits/MITRES18_006F10_26_0104_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-4-derivatives-and-limits/1_4.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0104_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-i-lecture-4-derivatives/id408737555?i=93802651>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/zKtYCGbCfSc>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-i-sets-functions-and-limits/lecture-4-derivatives-and-limits 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> A continuation of the previous lecture; important limit properties are developed as theorems from the formal definiton of 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-i-sets-functions-and-limits/lecture-5-a-more-rigorous-approach-to-limits/MITRES18_006F10_26_0105_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-5-a-more-rigorous-approach-to-limits/MITRES18_006F10_26_0105_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-5-a-more-rigorous-approach-to-limits/1_5.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0105_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-i-lecture-5-a-more-rigorous/id408737555?i=93802640>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/9tYUmwvLyIA>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-i-sets-functions-and-limits/lecture-5-a-more-rigorous-approach-to-limits 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 mathematical induction; some examples of what mathematical induction is and isn't; applications to limit 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-i-sets-functions-and-limits/lecture-6-mathematical-induction/MITRES18_006F10_26_0106_300k-mp4.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-6-mathematical-induction/MITRES18_006F10_26_0106_300k-mp4.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-006-calculus-revisited-single-variable-calculus-fall-2010/part-i-sets-functions-and-limits/lecture-6-mathematical-induction/1_6.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18_006F10/MITRES18_006F10_26_0106_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/unit-i-lecture-6-mathematical/id408737555?i=93802644>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/cm0io4R0tOM>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-i-sets-functions-and-limits/lecture-6-mathematical-induction 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