RES.18-007 Calculus Revisited: Multivariable Calculus | Part IV: Matrix AlgebraThis page includes five video lectures and links to associated lecture notes.
http://ocw.mit.edu/resources/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/part-iv
2013-01-22T06:47:38+05:00MIT OpenCourseWare http://ocw.mit.eduen-USContent 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.htmLecture 1: Linearity Revisited<p><strong>Video Description:</strong> Herb Gross considers linearity in spaces of dimension greater than 2, including a discussion of local linearity.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: "Nice" Functions, "Locally" Linear, Matrix of Coefficients, Matrix Multiplication<br><br>Thumbnail - <a href= http://img.youtube.com/vi/MfN1lqArwAg/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part4_lec1_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iv-matrix-algebra-lecture/id491034051?i=108768197>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/MfN1lqArwAg>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br>
http://ocw.mit.edu/resources/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/part-iv/lecture-1-linearity-revisited
Gross, Herbert2012-03-09T14:11:48+05:00en-US"Nice" Functions"Locally" LinearMatrix of CoefficientsMatrix MultiplicationMIT OpenCourseWare http://ocw.mit.eduContent 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.htmLecture 2: The "Game" of Matrices<p><strong>Video Description:</strong> Herb Gross describes the "game" of matrices — the rules of matrix arithmetic and algebra. He also covers non-singularity and the inverse of a matrix.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Definition of Addition, Definition of Multiplication, Definition of Equal, Differences from "usual" Algebra, Properties (Rules) of the Game, Non-Singular, Role of Determinants<br><br>Thumbnail - <a href= http://img.youtube.com/vi/rRCN5542U7E/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part4_lec2_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iv-matrix-algebra-lecture/id491034051?i=108768104>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/rRCN5542U7E>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br>
http://ocw.mit.edu/resources/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/part-iv/lecture-2-the-game-of-matrices
Gross, Herbert2012-03-09T14:11:48+05:00en-USDefinition of AdditionDefinition of MultiplicationDefinition of EqualDifferences from "usual" AlgebraProperties (Rules) of the GameNon-Singular, Role of DeterminantsMIT OpenCourseWare http://ocw.mit.eduContent 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.htmLecture 3: Inverting a Matrix<p><strong>Video Description:</strong> Herb Gross illustrates how to invert a square matrix and its relevance to Calculus of Several Variables.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Matrix Algebra Interpretation, Function Interpretation<br><br>Thumbnail - <a href= http://img.youtube.com/vi/sZh-zowKEQQ/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part4_lec3_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iv-matrix-algebra-lecture/id491034051?i=108768205>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/sZh-zowKEQQ>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br>
http://ocw.mit.edu/resources/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/part-iv/lecture-3-inverting-a-matrix
Gross, Herbert2012-03-09T14:11:48+05:00en-USMatrix Algebra InterpretationFunction InterpretationMIT OpenCourseWare http://ocw.mit.eduContent 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.htmLecture 4: Inverting More General Systems of Equations<p><strong>Video Description:</strong> Herb Gross demonstrates how to invert systems of non-linear equations.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Inverting More General Systems of Equations<br><br>Thumbnail - <a href= http://img.youtube.com/vi/a-w4F0c57nE/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part4_lec4_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iv-matrix-algebra-lecture/id491034051?i=108768196>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/a-w4F0c57nE>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br>
http://ocw.mit.edu/resources/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/part-iv/lecture-4-inverting-more-general-systems-of-equations
Gross, Herbert2012-03-09T14:11:48+05:00en-USInverting More General Systems of EquationsMIT OpenCourseWare http://ocw.mit.eduContent 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.htmLecture 5: Maxima and Minima in Several Variables<p><strong>Video Description:</strong> With our knowledge of matrix algebra to help, Herb Gross teaches how to find the local maxima and minima of functions of several real variables.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: How to Test for Max-Min Coordinates, Insufficient Information<br><br>Thumbnail - <a href= http://img.youtube.com/vi/io8kTsSnOdE/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part4_lec5_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iv-matrix-algebra-lecture/id491034051?i=108768190>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/io8kTsSnOdE>YouTube </a><br><br><a href= 'http://ocw.mit.edu/terms/'>(CC BY-NC-SA)</a><br><br>
http://ocw.mit.edu/resources/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/part-iv/lecture-5-maxima-and-minima-in-several-variables
Gross, Herbert2012-03-09T14:11:48+05:00en-USHow to Test for Max-Min CoordinatesInsufficient InformationMIT OpenCourseWare http://ocw.mit.eduContent 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