This page includes seven video lectures and links to associated lecture notes. http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-ii 2013-01-23T06:40:12+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>Track Description:</strong> Herb Gross defines and illustrates the different types of solutions of a differential equation: General solutions, particular solutions, and singular solutions.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: General Solution, Particular Solution, Singular Solution, Approach to 1st Order/1st Degree Equations, Exact Differential Equations, "Non-Exact" Equations<br><br>Thumbnail - <a href= http://img.youtube.com/vi/GQKFkoy4VOw/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part2_lec1_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-ii-differential-equations/id494296411?i=109307713>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/GQKFkoy4VOw>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-ii/lecture-1-the-concept-of-a-general-solution Gross, Herbert 2012-03-29T14:32:12+05:00 en-US General Solution Particular Solution Singular Solution Approach to 1st Order/1st Degree Equations Exact Differential Equations "Non-Exact" Equations 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>Track Description:</strong> Herb Gross defines and illustrates linear differential equations of order 2. Herb also shows how to find solutions of this type of equation.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Non-Linear Equations, Linear Equations, Properties of Linear Equations, Are there Other Types of Solutions?<br><br>Thumbnail - <a href= http://img.youtube.com/vi/IkpQJSDK940/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part2_lec2_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-ii-differential-equations/id494296411?i=109307684>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/IkpQJSDK940>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-ii/lecture-2-linear-differential-equations Gross, Herbert 2012-03-29T14:32:12+05:00 en-US Non-Linear Equations Linear Equations Properties of Linear Equations Are there Other Types of Solutions? 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>Track Description:</strong> Herb Gross talks about a specific type of Differential Equations, namely those that are linear, 2nd order, homogeneous and with constant coefficients. He gives examples of the three types of possible general solutions and then shows why they ARE the solutions.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Solving the Linear Equations L(y) = 0, Constant Coefficients<br><br>Thumbnail - <a href= http://img.youtube.com/vi/DJO6ilwbWiI/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part2_lec3_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-ii-differential-equations/id494296411?i=109307714>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/DJO6ilwbWiI>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-ii/lecture-3-solving-the-linear-equations-l-y-0-constant-coefficients Gross, Herbert 2012-03-29T14:32:12+05:00 en-US Solving the Linear Equations L(y) = 0 Constant Coefficients 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>Track Description:</strong> Herb Gross shows how to find particular (and general) solutions of second order linear differential equations with constant coefficients using the method of undetermined coefficients.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Finding A Particular Solution<br><br>Thumbnail - <a href= http://img.youtube.com/vi/dzKnv4ntH2g/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part2_lec4_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-ii-differential-equations/id494296411?i=109307712>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/dzKnv4ntH2g>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-ii/lecture-4-undetermined-coefficients Gross, Herbert 2012-03-29T14:32:12+05:00 en-US Finding A Particular Solution 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>Track Description:</strong> Herb Gross uses the method of Variation of Parameters to find a particular solution of linear homogeneous order 2 differential equations when the general solution is known.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Variations of Parameters<br><br>Thumbnail - <a href= http://img.youtube.com/vi/IYKULUq6YPQ/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part2_lec5_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-ii-differential-equations/id494296411?i=109307715>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/IYKULUq6YPQ>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-ii/lecture-5-variations-of-parameters Gross, Herbert 2012-03-29T14:32:12+05:00 en-US Variations of Parameters 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>Track Description:</strong> Herb Gross show how to find the general solution of a linear, homogeneous differential equation of order 2 when the coefficients are analytic functions.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Undetermined Coefficients, Constant Coefficients, When Coefficients Are Not Constant<br><br>Thumbnail - <a href= http://img.youtube.com/vi/oY0ItxI9xTk/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part2_lec6_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-ii-differential-equations/id494296411?i=109307717>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/oY0ItxI9xTk>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-ii/lecture-6-power-series-solutions Gross, Herbert 2012-03-29T14:32:12+05:00 en-US Undetermined Coefficients Constant Coefficients When Coefficients Are Not Constant 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>Track Description:</strong> Herb Gross describes and justifies the use of Laplace Transforms as a method of solving linear differential equations with given initial conditions.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: "Comparison Test", Linearity, Application to Linear Differential Equations (Constant Coefficients, Lerch's Theorem)<br><br>Thumbnail - <a href= http://img.youtube.com/vi/an5E940fqZQ/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part2_lec7_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-ii-differential-equations/id494296411?i=109307688>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/an5E940fqZQ>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br> http://ocw.mit.edu/resources/res-18-008-calculus-revisited-complex-variables-differential-equations-and-linear-algebra-fall-2011/part-ii/lecture-7-laplace-transforms Gross, Herbert 2012-03-29T14:32:12+05:00 en-US "Comparison Test" Linearity Application to Linear Differential Equations (Constant Coefficients, Lerch's Theorem) 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