Mathematics 133
Notes from October 12, 2020, lecture session

The recording for this lecture is available online as 
 http://math.ucr.edu/~res/math133-2020/Oct12.mp4 .
Please note that this file is quite large, so downloading might take some time and there might be storage problems on your devices.
The recommended homework exercises for Chapter 1 are posted in the following file:  http://math.ucr.edu/~res/math133-2020/week2/sections_1.4-1.5/math133hw1.pdf

 Relevant directory files:
Here is a listing with comments on their significance.  These links are all clickable.  Copies of most files from http://math.ucr.edu/~res/math133-2020/week1 can also be found in http://math.ucr.edu/~res/math133-2020/week2/sections_1.4-1.5.
http://math.ucr.edu/~res/math133-2020/week1/geometrynotes01.f13.pdf   The first chapter of the course notes.   The lecture covered Sections I.4 and I.5.
https://math.ucr.edu/~res/math133-2020/week1/Whiteboard.oct.07-3.png  Edited version of a whiteboard created during the October 5 lecture.  This file poses a basic question motivating the material in Section I.4.
https://math.ucr.edu/~res/math133-2020/week1/Whiteboard.oct.07-4.png  Edited version of a whiteboard created during the October 5 lecture.  This file suggests how one might consider the question in the preceding document for the special case of lines. 
https://math.ucr.edu/~res/math133-2020/week1/examples0104.pdf   Worked out example of a geometric problem solved using vector methods. 
https://math.ucr.edu/~res/math133-2020/week1/centroids.pdf   Explanation of the physical meaning for the mathematical concept of  "barycenter" or "centroid."
https://math.ucr.edu/~res/math133-2020/week1/examples0106.pdf   Worked out example of finding the barycentric coordinates of one point in the coordinate plane with respect to a given triple of noncollinear points.  
https://math.ucr.edu/~res/math133-2020/week1/examples0106a.pdf   Drawing for the preceding example. 
https://math.ucr.edu/~res/math133-2020/week1/examples0101.pdf   Solved problem using vector methods to find the bisector of an angle.  
https://math.ucr.edu/~res/math133-2020/week1/examples0101a.pdf   Commentary on the preceding file.
https://math.ucr.edu/~res/math133-2020/week2/sections_1.4-1.5/Whiteboard.oct.12-1.png  Edited version of a whiteboard created during the October 12 lecture.  This file gives a drawing for the final example in Section I.5.
https://math.ucr.edu/~res/math133-2020/week2/sections_1.4-1.5/linalg8.pdf   Chapter from the current Math 031 textbook which discusses barycentric coordinates and related topics.  The discussion is more formal and thorough than in the notes, and there are additional exercises. 
https://math.ucr.edu/~res/math133-2020/week2/sections_1.4-1.5/linalg8a.pdf   Solutions for the odd numbered exercises in the preceding document.
https://math.ucr.edu/~res/math133-2020/week2/sections_1.4-1.5/math133hw01.pdf   This file contains the strongly recommended assignments for Chapter I.  Problems at roughly comparable levels of difficulty can be expected on quizzes and examinations.