http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus 2013-01-12T07:13:49+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>Calculus is about change. One function tells how quickly another function is changing. Professor Strang shows how calculus applies to ordinary life situations, such as:</p> <ul> <li style="list-style: disc outside none;">driving a car</li> <li style="list-style: disc outside none;">climbing a mountain</li> <li style="list-style: disc outside none;">growing to full adult height</li> </ul> <p>Professor Strang's Calculus textbook (1st edition, 1991) is freely available <a href="/resources/res-18-001-calculus-online-textbook-spring-2005">here</a>.</p> <p>Subtitles are provided through the generous assistance of Jimmy Ren.</p>Transcript: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-of-calculus/MITRES18_005S10_big_picture_calculus_transcript.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-of-calculus/big_picture_calculus_512kb.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-of-calculus/Big_Picture_of_Calculus.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18.005/big_picture_calculus_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://www.apple.com/downloads/dashboard/calculate_convert/livemathvectorcalculuswidget.html>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/UcWsDwg1XwM>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-of-calculus Strang, Gilbert 2010-04-30T12:11:42+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>Calculus finds the relationship between the distance traveled and the speed &mdash; easy for constant speed, not so easy for changing speed. Professor Strang is finding the &quot;rate of change&quot; and the &quot;slope of a curve&quot; and the &quot;derivative of a function.&quot;</p><p>Professor Strang's Calculus textbook (1st edition, 1991) is freely available <a href="/resources/res-18-001-calculus-online-textbook-spring-2005">here</a>.</p><p>Subtitles are provided through the generous assistance of Jimmy Ren.</p>Transcript: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-derivatives/MITRES18_005S10_big_picture_derivatives_transcript.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-derivatives/big_picture_derivatives_512kb.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-derivatives/Big_Picture_Derivatives.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18.005/big_picture_derivatives_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/big-picture-derivatives/id385157068?i=85275394>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/T_I-CUOc_bk>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-derivatives Strang, Gilbert 2010-04-30T12:11:42+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>At the top and bottom of a curve (Max and Min), the slope is zero. The &quot;second derivative&quot; shows whether the curve is bending down or up. Here is a real-world example of a minimum problem:<br /> <br /> <em>What route from home to work takes the shortest time?</em></p> <p>Professor Strang's Calculus textbook (1st edition, 1991) is freely available <a href="/resources/res-18-001-calculus-online-textbook-spring-2005">here</a>.</p> <p>Subtitles are provided through the generous assistance of Jimmy Ren.</p>Transcript: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/max-and-min-and-second-derivative/max_min_second_der_512kb.srt>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/max-and-min-and-second-derivative/max_min_second_der_512kb.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/max-and-min-and-second-derivative/Max_Min.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18.005/max_min_second_der_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/max-min-second-derivative/id385157068?i=85275393>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/tBBJ2TSTa1Q>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/max-and-min-and-second-derivative Strang, Gilbert 2010-04-30T12:11:42+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>Professor Strang explains how the &quot;magic number <em>e</em>&quot; connects to ordinary things like the interest on a bank account. The graph of<br /> y = e^x has the special property that its slope equals its height (it goes up &quot;exponentially fast&quot;!). This is the great function of calculus.</p><p>Professor Strang's Calculus textbook (1st edition, 1991) is freely available <a href="/resources/res-18-001-calculus-online-textbook-spring-2005">here</a>.</p><p>Subtitles are provided through the generous assistance of Jimmy Ren.</p>Transcript: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/the-exponential-function/MITRES18_005S10_exponential_e_transcript.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/the-exponential-function/exponential_e_512kb.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/the-exponential-function/exponential_function.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18.005/exponential_e_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/the-exponential-function/id385157068?i=85275395>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/oo1ZZlvT2LQ>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/the-exponential-function Strang, Gilbert 2010-04-30T12:11:42+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>The second half of calculus looks for the distance traveled even when the speed is changing. Finding this &quot;integral&quot; is the opposite of finding the derivative. Professor Strang explains how the integral adds up little pieces to recover the total distance.<br /> <br /> <em>I know the speed at each moment of my trip, so how far did I go?</em></p><p>Professor Strang's Calculus textbook (1st edition, 1991) is freely available <a href="/resources/res-18-001-calculus-online-textbook-spring-2005">here</a>.</p><p>Subtitles are provided through the generous assistance of Jimmy Ren.</p>Transcript: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-integrals/MITRES18_005S10_big_picture_integrals_transcript.pdf>PDF (English - US)</a><br>Subtitles: <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-integrals/big_picture_integrals_512kb.srt>SRT (English - US)</a><br>Thumbnail - <a href= /resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-integrals/Big_Picture_Integrals.jpg>JPG (OCW)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES18.005/big_picture_integrals_512kb.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/podcast/big-picture-integrals/id385157068?i=85275390>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/2qxY859dzzQ>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-005-highlights-of-calculus-spring-2010/highlights_of_calculus/big-picture-integrals Strang, Gilbert 2010-04-30T12:11:42+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