Analytic geometry | Area | Vectors (mathematics and physics)
In 3-dimensional geometry and vector calculus, an area vector is a vector combining an area quantity with a direction, thus representing an oriented area in three dimensions. Every bounded surface in three dimensions can be associated with a unique area vector called its vector area. It is equal to the surface integral of the surface normal, and distinct from the usual (scalar) surface area. Vector area can be seen as the three dimensional generalization of signed area in two dimensions. (Wikipedia).
This video explains the definition of a vector space and provides examples of vector spaces.
From playlist Vector Spaces
Vector Calculus 1: What Is a Vector?
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Vector Calculus
Multivariable Calculus | The notion of a vector and its length.
We define the notion of a vector as it relates to multivariable calculus and define its length. http://www.michael-penn.net http://www.randolphcollege.edu/mathematics/
From playlist Vectors for Multivariable Calculus
What is a Vector Space? (Abstract Algebra)
Vector spaces are one of the fundamental objects you study in abstract algebra. They are a significant generalization of the 2- and 3-dimensional vectors you study in science. In this lesson we talk about the definition of a vector space and give a few surprising examples. Be sure to su
From playlist Abstract Algebra
Linear Algebra for Computer Scientists. 1. Introducing Vectors
This computer science video is one of a series on linear algebra for computer scientists. This video introduces the concept of a vector. A vector is essentially a list of numbers that can be represented with an array or a function. Vectors are used for data analysis in a wide range of f
From playlist Linear Algebra for Computer Scientists
What is a Vector Space? Definition of a Vector space.
From playlist Linear Algebra
Ex: Find the Magnitude of a Vector in 3D
This video explains how to determine the magnitude of a vector in 3D. Site: http://mathispower4u.com
From playlist Vectors in Space (3D)
Vectors | Lecture 1 | Vector Calculus for Engineers
Defines vectors, vector addition and vector subtraction. Join me on Coursera: https://www.coursera.org/learn/vector-calculus-engineers Lecture notes at http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_con
From playlist Vector Calculus for Engineers
This video introduces the Linear Algebra approach to area, and to volume. It also introduces bi-vectors, with applications from physics: torque, angular momentum and motion in a magnetic field. NJ Wildberger is also the developer of Rational Trigonometry: a new and better way of learning
From playlist A first course in Linear Algebra - N J Wildberger
Linear Algebra 14TBD: Calculation of Areas and Volumes by the Determinant
https://bit.ly/PavelPatreon https://lem.ma/LA - Linear Algebra on Lemma http://bit.ly/ITCYTNew - Dr. Grinfeld's Tensor Calculus textbook https://lem.ma/prep - Complete SAT Math Prep
From playlist Part 2 Linear Algebra: An In-Depth Course with a Focus on Applications
Lecture 13: Smooth Surfaces II (Discrete Differential Geometry)
Full playlist: https://www.youtube.com/playlist?list=PL9_jI1bdZmz0hIrNCMQW1YmZysAiIYSSS For more information see http://geometry.cs.cmu.edu/ddg
From playlist Discrete Differential Geometry - CMU 15-458/858
Area of a Parallelogram using 2 Vectors and Cross Product
Using basic Geometry I show you how the formula for the magnitude of a vector cross product is also how you find the area of a parallelogram using the Cross Product. Example) Finding the area of a parallelogram by find the magnitude of the cross product of two vectors. 9:06 My Vector Le
From playlist Vector Math Lessons
What is a Tensor? Lesson 38: Visualization of Forms: Tacks and Sheaves. And Honeycombs.
What is a Tensor? Lesson 38: Visualization of Forms Part 2 Continuing to complete the "visualization" of the four different 3-dimensional vector spaces when dim(V)=3. Erratta: Note: When the coordinate system is expanded the density of things *gets numerically larger* and the area/volum
From playlist What is a Tensor?
The Cross Product and Meister's Formula b) | Algebraic Calculus One | Wild Egg
In this lecture, we continue our discussion of cross products of planar vectors and move towards a famous and useful formula of J. Meister. This is a lecture in the Algebraic Calculus One course, which will present an exciting new approach to calculus, sticking with rational numbers and
From playlist Algebraic Calculus One from Wild Egg
The Cross Product and Meister's Formula | Algebraic Calculus One | Wild Egg
In this lecture, we introduce the cross product of two planar vectors: a somewhat novel notion that allows us to establish the signed area notion for general triangles. We are touching base with linear algebraic ideas here in establishing the linearity and skew-symmetric properties of the
From playlist Algebraic Calculus One from Wild Egg
Transformations and Signed Areas | Algebraic Calculus One | Wild Egg
We are moving towards understanding the signed area of a curve: a fundamental object in the Algebraic Calculus. Here we introduce transformations of the usual signed area: what happens when you translate a spline, and what happens when you apply a linear transformation to a spline: how do
From playlist Algebraic Calculus One
ME564 Lecture 25: Stokes' theorem and conservative vector fields
ME564 Lecture 25 Engineering Mathematics at the University of Washington Stokes' theorem and conservative vector fields Notes: http://faculty.washington.edu/sbrunton/me564/pdf/L25.pdf Course Website: http://faculty.washington.edu/sbrunton/me564/ http://faculty.washington.edu/sbrunton/
From playlist Engineering Mathematics (UW ME564 and ME565)
QED Prerequisites Geometric Algebra 4: The antisymmetric part
After a short rehash of the last lesson, we first have another look at the component-based demonstration that the symmetric part of the spacetime product of two 4-vectors. Then we study the antisymmetric part of the spacetime product and commit to interpreting this antisymmetric part as th
From playlist QED- Prerequisite Topics
linear algebra vector space (25 examples)
Vector Spaces. Definition and 25 examples. Featuring Span and Nul. Hopefully after this video vector spaces won't seem so mysterious any more! Check out my Vector Space playlist: https://www.youtube.com/watch?v=mU7DHh6KNzI&list=PLJb1qAQIrmmClZt_Jr192Dc_5I2J3vtYB Subscribe to my channel:
From playlist Vector Spaces