RES.18-007 Calculus Revisited: Multivariable Calculus | Part I: Vector ArithmeticThis page includes six video lectures and links to associated lecture notes.
http://ocw.mit.edu/resources/res-18-007-calculus-revisited-multivariable-calculus-fall-2011/part-i
2013-01-22T06:47:37+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 "Game" of Mathematics<p><strong>Video Description:</strong> Herb Gross introduces Calculus Revisited II — Functions of Several Variables — and discusses the over-arching theme "The Game of Mathematics". A game has objectives, rules, and definitions as well as strategies (logical plans) for meeting the objectives of the game. A mathematical structure is identical with the objective being to model real-world experience.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: What is a Game?, A New Look at Counting, Mathematical Structure, What is Truth?, Predetermined Rules<br><br>Thumbnail - <a href= http://img.youtube.com/vi/wsOoClvZmic/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part1_lec1_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-vector-arithmetic-lecture/id491034051?i=108768195>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/wsOoClvZmic>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-i/lecture-1-the-game-of-mathematics
Gross, Herbert2012-03-09T14:11:48+05:00en-USWhat is a Game?A New Look at CountingMathematical StructureWhat is Truth?Predetermined RulesMIT 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: "Arrow" Arithmetic<p><strong>Video Description:</strong> Herb Gross reviews the definition of vectors — objects that have magnitude, direction, and sense. He also defines equality of vectors, their components, and rules of arithmetic. Vector arithmetic shares many structural properties with scalar arithmetic including a zero and additive inverse. This video also covers the multiplication of a vector times a scalar.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Arrow Arithmetic, Vector Magnitude, Vector Direction, Vector Sence, Signed Numbers, Equality of Arrows, Addition of Vectors, i and j components, Scalar Multiplication, The Zero Vector, The Additive Inverse<br><br>Thumbnail - <a href= http://img.youtube.com/vi/nFf_SJRwfaY/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part1_lec2_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-vector-arithmetic-lecture/id491034051?i=115512009>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/nFf_SJRwfaY>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-i/lecture-2-arrow-arithmetic
Gross, Herbert2012-03-09T14:11:48+05:00en-USArrow ArithmeticVector MagnitudeVector DirectionVector SenceSigned NumbersEquality of ArrowsAddition of Vectorsi and j componentsScalar MultiplicationThe Zero VectorThe Additive InverseMIT 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: Three-Dimensional Vectors<p><strong>Video Description:</strong> Herb Gross introduces 3-dimensional vectors — those with 3 othogonal components (x, y, z directions). This video also covers 3-dimensional magnitude and arithmetic in Cartesian coordinates (not polar coordinates). Prof. Gross also explains how 3-dimensional vectors are structurally the same as 2-dimensional vectors.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: 3-Dimensional Vectors, Name-Versus-Concept, Polar Coordinates<br><br>Thumbnail - <a href= http://img.youtube.com/vi/JAxRgACOQtA/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part1_lec3_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-vector-arithmetic-lecture/id491034051?i=115512008>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/JAxRgACOQtA>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-i/lecture-3-three-dimensional-vectors
Gross, Herbert2012-03-09T14:11:48+05:00en-US3-Dimensional VectorsName-Versus-ConceptPolar CoordinatesMIT 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: The Dot Product<p><strong>Video Description:</strong> Herb Gross motivates the definition of the dot product: Work = Force x Distance. He also shows how to calculate the dot product of two vectors in 3-space. Other topics include projections, directional cosines, and the arithmetic structure of the dot product.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: The Dot Product, Cartesian Coordinates, Law of Cosines, Projections, Directional Cosines<br><br>Thumbnail - <a href= http://img.youtube.com/vi/y9Sa8StSX-M/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part1_lec4_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-vector-arithmetic-lecture/id491034051?i=108768108>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/y9Sa8StSX-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-18-007-calculus-revisited-multivariable-calculus-fall-2011/part-i/lecture-4-the-dot-product
Gross, Herbert2012-03-09T14:11:48+05:00en-USThe Dot ProductCartesian CoordinatesLaw of CosinesProjectionsDirectional CosinesMIT 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: The Cross Product<p><strong>Video Description:</strong> Herb Gross defines the arithmetic structure of the cross product of two vectors. He then provides an interpretation of the magnitude of cross product as area. He concludes with a brief look at determinants.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: The Cross Product, Very Brief Look at Determinants<br><br>Thumbnail - <a href= http://img.youtube.com/vi/Yw8vBDhVs8o/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part1_lec5_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-vector-arithmetic-lecture/id491034051?i=108768102>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Yw8vBDhVs8o>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-i/lecture-5-the-cross-product
Gross, Herbert2012-03-09T14:11:48+05:00en-USThe Cross ProductVery Brief Look at 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 6: Equations of Lines & Planes<p><strong>Video Description:</strong> Herb Gross discusses the topic of equations of lines and planes in 3-dimensional space. Topics include: The normal vector to a plane; Parallel planes; Equation of a plane; Equation of a line in space.</p> <p><strong>Instructor/speaker:</strong> Prof. Herbert Gross</p>Keywords: Equations of Lines and Planes<br><br>Thumbnail - <a href= http://img.youtube.com/vi/Brmq13Waa_Y/default.jpg>JPG (YouTube)</a><br>Video - download: <a href= http://www.archive.org/download/MITRES.18-007/MITRES_18-007_Part1_lec6_300k.mp4>Internet Archive (MP4)</a><br>Video - download: <a href= http://itunes.apple.com/us/itunes-u/part-i-vector-arithmetic-lecture/id491034051?i=108768200>iTunes U (MP4)</a><br>Video - stream: <a href= http://www.youtube.com/v/Brmq13Waa_Y>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-i/lecture-6-equations-of-lines-planes
Gross, Herbert2012-03-09T14:11:48+05:00en-USEquations of Lines and PlanesMIT 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