RES.18-008 Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra | Part III: Linear AlgebraThis page includes eight 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-iii
2013-01-23T06:40:13+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: Vector Spaces<p><strong>Track Description:</strong> Herb Gross describes and illustrates the axiomatic definition of a vector space and discusses subspaces.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Structural (Axiomatic) Definition, Subspaces<br><br>Thumbnail - <a href= http://img.youtube.com/vi/KvQkRX1nIqQ/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part3_lec1_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iii-linear-algebra-lecture/id494296411?i=109307682>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/KvQkRX1nIqQ>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-iii/lecture-1-vector-spaces
Gross, Herbert2012-03-29T14:32:12+05:00en-USStructural (Axiomatic) DefinitionSubspacesMIT 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: Spanning Vectors<p><strong>Track Description:</strong> Herb Gross describes spanning vectors: Vectors whose linear combinations generate a vector space. Herb also defines linear dependence and the dimension of a vector space.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Definition/Equivalent Definition, Linear Dependence, Linear Independence, Dimension Revisited, Infinite Dimensional Vector Space<br><br>Thumbnail - <a href= http://img.youtube.com/vi/anICA1XFJ_M/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part3_lec2_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iii-linear-algebra-lecture/id494296411?i=109307680>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/anICA1XFJ_M>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-iii/lecture-2-spanning-vectors
Gross, Herbert2012-03-29T14:32:12+05:00en-USDefinition/Equivalent DefinitionLinear DependenceLinear IndependenceDimension RevisitedInfinite Dimensional Vector SpaceMIT 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: Constructing Bases<p><strong>Track Description:</strong> Herb Gross gives a short review of bases and dimension. He then does an example using the row-reduced matrix technique.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Row-Reduced Matrix Technique<br><br>Thumbnail - <a href= http://img.youtube.com/vi/l59IX58Wce8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part3_lec3_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iii-linear-algebra-lecture/id494296411?i=109307689>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/l59IX58Wce8>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-iii/lecture-3-constructing-bases
Gross, Herbert2012-03-29T14:32:12+05:00en-USRow-Reduced Matrix TechniqueMIT 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: Linear Transformations<p><strong>Track Description:</strong> Herb Gross defines Linear Transformations from vector space <em>V</em> into vector space <em>W</em>. He also defines and gives examples of the null space of such a map and illustrates the matrix representation of a linear transformation relative to a given basis.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Linear Transformations, Null Space<br><br>Thumbnail - <a href= http://img.youtube.com/vi/6UXba5MKsfc/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part3_lec4_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iii-linear-algebra-lecture/id494296411?i=109307687>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/6UXba5MKsfc>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-iii/lecture-4-linear-transformations
Gross, Herbert2012-03-29T14:32:12+05:00en-USLinear TransformationsNull SpaceMIT 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: Determinants<p><strong>Track Description:</strong> Herb Gross examines the determinant in the framework of vector spaces. He shows us how the value of a particular determinant tells us whether a given set of vectors is a basis of a given vector space with a known basis.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Generalization, "Short-Cut" (Row-Reduction)<br><br>Thumbnail - <a href= http://img.youtube.com/vi/CEbrxYGpfZY/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part3_lec5_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iii-linear-algebra-lecture/id494296411?i=109307683>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/CEbrxYGpfZY>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-iii/lecture-5-determinants
Gross, Herbert2012-03-29T14:32:12+05:00en-USGeneralization"Short-Cut" (Row-Reduction)MIT 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 6: Eigenvectors<p><strong>Track Description:</strong> Herb Gross defines an eigenvector of a linear map ƒ as a vector <em>x</em> that is mapped into a constant multiple, <em>c</em>, of itself. The value of <em>c</em> is called the eigenvalue (or characteristic) for the corresponding vector <em>x</em>.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: "Brute-Force" Technique, Geometric Interpretation, Matrix Approach<br><br>Thumbnail - <a href= http://img.youtube.com/vi/Bk9SZMsPEHk/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part3_lec6_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iii-linear-algebra-lecture/id494296411?i=109307679>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Bk9SZMsPEHk>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-iii/lecture-6-eigenvectors
Gross, Herbert2012-03-29T14:32:12+05:00en-US"Brute-Force" TechniqueGeometric InterpretationMatrix ApproachMIT 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 7: Dot Products<p><strong>Track Description:</strong> Herb Gross axiomatically defines the dot product as the map of ordered pairs of vectors into the real numbers. Using this definition, Herb next defines and shows how and why to find an orthonormal basis.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Gram-Schmidt Orthogonalization Process<br><br>Thumbnail - <a href= http://img.youtube.com/vi/anA3P9McG5Y/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part3_lec7_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iii-linear-algebra-lecture/id494296411?i=109307716>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/anA3P9McG5Y>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-iii/lecture-7-dot-products
Gross, Herbert2012-03-29T14:32:12+05:00en-USGram-Schmidt Orthogonalization ProcessMIT 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 8: Orthogonal Functions<p><strong>Track Description:</strong> Herb Gross defines and illustrates the Fourier representation of a piecewise continuous function.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Fourier Representation, Contrast with Power Series<br><br>Thumbnail - <a href= http://img.youtube.com/vi/ZYf0tz9oVz8/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part3_lec8_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-iii-linear-algebra-lecture/id494296411?i=109307678>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/ZYf0tz9oVz8>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-iii/lecture-8-orthogonal-functions
Gross, Herbert2012-03-29T14:32:12+05:00en-USFourier RepresentationContrast with Power SeriesMIT 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