RES.18-008 Calculus Revisited: Complex Variables, Differential Equations, and Linear Algebra | Part I: Complex VariablesThis page includes five 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-i
2013-01-23T06:40:12+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: The Complex Numbers<p><strong>Track Description:</strong> Herb Gross explains the need to define complex numbers. He defines the structure of the system of complex numbers including addition, subtraction, multiplication, division, powers and roots and shows that the system is closed under all these operations.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: System of Integers, Real Numbers, Complex Numbers, Additional Structure of Complex Numbers, Multiplication in Polar Coordinates, DeMoivre's Theroem, Extracting Roots<br><br>Thumbnail - <a href= http://img.youtube.com/vi/BOx8LRyr8mU/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part1_lec1_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-complex-variables-lecture/id494296411?i=109307711>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/BOx8LRyr8mU>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-i/lecture-1-the-complex-numbers
Gross, Herbert2012-03-29T14:32:12+05:00en-USSystem of IntegersReal NumbersComplex NumbersAdditional Structure of Complex NumbersMultiplication in Polar CoordinatesDeMoivre's TheroemExtracting RootsMIT 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: Functions of a Complex Variable<p><strong>Track Description:</strong> Herb Gross discusses functions of a complex variable, limits, derivatives and the Cauchy-Riemann conditions. Functions of a complex variable that are differentiable everywhere are called analytic functions.</p>
<p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Introduction to Derivatives<br><br>Thumbnail - <a href= http://img.youtube.com/vi/rVvGqWyQB_0/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part1_lec2_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-complex-variables-lecture/id494296411?i=109307686>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/rVvGqWyQB_0>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-i/lecture-2-functions-of-a-complex-variable
Gross, Herbert2012-03-29T14:32:12+05:00en-USIntroduction to DerivativesMIT 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: Conformal Mappings<p><strong>Track Description:</strong> Herb Gross defines and explains what is meant by a conformal mapping.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Invertible Mappings, Conformal Maps and Laplace's Equation, Locally Invertible, Chain Rule, Symmetry<br><br>Thumbnail - <a href= http://img.youtube.com/vi/s1DFa1dCss0/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part1_lec3_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-complex-variables-lecture/id494296411?i=109307710>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/s1DFa1dCss0>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-i/lecture-3-conformal-mappings
Gross, Herbert2012-03-29T14:32:12+05:00en-USInvertible MappingsConformal Maps and Laplace's EquationLocally InvertibleChain RuleSymmetryMIT 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: Sequences and Series<p><strong>Track Description:</strong> Herb Gross defines complex valued functions by means of power series expansions. He shows us how the amazing identity of DeMoivre is derived.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Application to "Real" Series<br><br>Thumbnail - <a href= http://img.youtube.com/vi/UGiED1HPB08/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part1_lec4_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-complex-variables-lecture/id494296411?i=109307681>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/UGiED1HPB08>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-i/lecture-4-sequences-and-series
Gross, Herbert2012-03-29T14:32:12+05:00en-USApplication to "Real" 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.htmLecture 5: Integrating Complex Functions<p><strong>Track Description:</strong> Herb Gross generalizes the definition of the integral of a real-valued function of a real variable to the integral of a complex-valued function of a complex variable and examines the ramifications of this generalization.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Method #1, "Rubber Sheet" Geometry (Topology), Method #2<br><br>Thumbnail - <a href= http://img.youtube.com/vi/gpZu5N1FFq0/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-008/MITRES_18-008_Part1_lec5_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-complex-variables-lecture/id494296411?i=109307685>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/gpZu5N1FFq0>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-i/lecture-5-integrating-complex-functions
Gross, Herbert2012-03-29T14:32:12+05:00en-USMethod #1"Rubber Sheet" Geometry (Topology)Method #2MIT 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