Calculus Revisited Part 2: Functions Of Several Variables - Unit 1, Lecture 2, Arrow Arithmetic
Channel: usephniel
Date: 2012-09-07

A slightly touched-up version of the other version available on Youtube, with corrected light levels and improved contrast.

Calculus Revisited Videos Part 2 - Functions of Several Variables
 
The Game of Mathematics       

Block 1: Mathematical Structure and Vectors

Professor Gross introduces the arithmetic of vectors in terms of the structure of a game. In particular, he shows how the arithmetic of vectors helps us define planes and lines analytically.

Note that this series, Calculus Revisited Part 2, fits in the MIT Open Courseware lecture series: http://www.youtube.com/watch?v=elputTS7tAA&playnext=1&list=PL3B08AE665AB9002A&feature=results_main

Block 1: Mathematical Structure and Vectors (this block)
1) The Game of Mathematics
2) Vectors Revisited - Arrow Arithmetic (this lecture)
3) 3-dimensional Vectors
4) The Dot Product
5) The Cross Product
6) Lines and Planes

Block 2: Functions
1) Vector Functions of Scalar Variables
2) Tangent and Normal Vectors
3) Polar Coordinates
4) Vectors and Polar Coordinates

Block 3: Real Valued Functions of Several Real Variables
1) n-Dimensional Vector Spaces
2) Introduction to the Calculus of Several Variables
3) The Directional Derivative
4) The Chain Rule
5) Integrals Involving Parameters
6) Exact Differentials

Block 4: Matrix Algebra
1) Linearity Revisited
2) Matrix Algebra
3) Inverting a Square Matrix
4) Inverting General Systems of Equations
5) Max-min Problems in Several Variables

Block 5: Line Integrals along closed curves (Green's Theorem)
1) Double (Multiple) Sums
2) The Fundamental Theorem
3) Multiple Integrals and the Jacobian
4) Line Integrals
5) Green's Theorem

I am uploading this video to Youtube per the terms of the Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 license, from the video's Internet Archive repository, where the rights-holders shared it:
http://archive.org/details/VectorsRevisited-ArrowArithmetic

Thanks also to the "Mathematics As A Second Language" website, which linked to and provided context for the here-to-for missing (from Youtube) videos from the series: http://www.adjectivenounmath.com/id93.html

Aside from the Creative Commons license, as stipulated by archive.org, the video's original 1971 copyright is indicated as belonging to MIT's Center for Advanced Engineering Study. Please consider making a donation to MIT's OpenCourseware initiative at ocw.mit.edu.