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What you'll learn?

  • Fundamentals of vector algebra: vector addition & subtraction
  • Scalar Product
  • Vector Product
  • Vector Projection
  • The Levi-Civita Operator
  • Differential Operators

Course Overview

Vector algebra is an Essential Topic for most science fields like engineering, mathematics and physics with a critical use.

in physics, we use the vectors to describe velocity, momentum, acceleration, position, etc.

this course will cover the fundamentals of the vector algebra and implementation of vectors algebra in a various field in mathematics.

 

gaining the maximal benefit in this course will be through practicing. in every exercise you need to try figure out how to solve before watching the solution.

you will definitely have a hard time trying to figure out how to solve it. However, when you got the "Ah,Ha" moment sure you will feel the passion to continue practicing.    

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Pre-requisites

  • Basic mathematical Knowledge

Target Audience

  • Engineering, mathematics and science major students
  • Those who want to expand their mathematical knowledge
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Curriculum 66 Lectures 02:26:19

  • Section 1 : Introduction 10 Lectures 00:18:23

    • Lecture 1 :
    • Lecture 2 :
    • Vector vs Scalar
    • Lecture 3 :
    • Representation of Vectors
    • Lecture 4 :
    • Vector Types
    • Lecture 5 :
    • Vector Addition
    • Lecture 6 :
    • Vector Subtraction & Addition Properties
    • Lecture 7 :
    • The Unit Vector
    • Lecture 8 :
    • Vector Shifting
    • Lecture 9 :
    • Vector Magnitude
    • Lecture 10 :
    • Vector Direction

  • Section 2 : Product of Vectors 5 Lectures 00:25:18

    • Lecture 1 :
    • Section Preview
    • Lecture 2 :
    • Scalar Product
    • Lecture 3 :
    • Projection
    • Lecture 4 :
    • Vector Product
    • Lecture 5 :
    • Analytical Form of Vector Product

  • Section 3 : The Index Notation 4 Lectures 00:13:36

    • Lecture 1 :
    • Section Preview
    • Lecture 2 :
    • The kronecker delta
    • Lecture 3 :
    • Einstein summation convention
    • Lecture 4 :
    • The Livi-Civita Operator

  • Section 4 : 3D Differential Operators 5 Lectures 00:07:37

    • Lecture 1 :
    • Section Preview
    • Lecture 2 :
    • The Gradient
    • Lecture 3 :
    • The Divergence
    • Lecture 4 :
    • The Rotor
    • Lecture 5 :
    • The Laplacian

  • Section 5 : Practice The Fundamentals 21 Lectures 00:34:32

    • Lecture 1 :
    • Section Preview
    • Lecture 2 :
    • Problem #1
      • Given the two vectors: u = (1,2) , v = (3,7) find: a. Magnitude of u and v b. the dot product between the vectors. c. the interior angle between the two vectors. d. are the vector orthogonal? why?
    • Lecture 3 :
    • Solution for Problem #1
    • Lecture 4 :
    • Problem #2
      • Given the two vectors: u = (cosθ,sinθ) v = (sinθ,-cosθ) the vectors are: a. parallel b. orthogonal c. nether parallel nor orthogonal
    • Lecture 5 :
    • Solution for Problem #2
    • Lecture 6 :
    • Problem #3
      • Given three vectors: u = (1,2,-3) v = (4,-3,1) w = (2,1,0) in each given expression, determine is the result: a. vector. c. scalar. c. undefined. if its defined expression, find the result. 1. (u w) x v 2. (u v) x (v w) 3. (u x v) x (w x u)
    • Lecture 7 :
    • Solution for Problem #3
    • Lecture 8 :
    • Problem #4
      • Given: |w x u | = 7. describe the angle between w and u in terms of the magnitude of w and u
    • Lecture 9 :
    • Solution for Problem #4
    • Lecture 10 :
    • Problem #5
      • Given the two vectors: u,v What can be said about the vectors under each condition? 1. The projection of u into v equals u . 2. The projection of u into v equals 0 .
    • Lecture 11 :
    • Solution for Problem #5
    • Lecture 12 :
    • Problem #6
      • Given the vectors: u = (1,-1,4) , v = (2,6,1) are the vectors orthogonal?
    • Lecture 13 :
    • Solution for Problem #6
    • Lecture 14 :
    • Problem #7
      • Given two vectors: u=(-3,-2) , v = (-4,-1) find the projection of v into u and write u as sum of two orthogonal vectors
    • Lecture 15 :
    • Solution for Problem #7
    • Lecture 16 :
    • Problem #8
      • Prove: || u - v ||^2  = || u ||^2 + || v||^2 - 2(uv)
    • Lecture 17 :
    • Solution for Problem #8
    • Lecture 18 :
    • Problem #9
      • Given the two vectors: a = 2i + 4j - 7k , b = 2i + 6j + xk find x such that the vectors are perpendicular
    • Lecture 19 :
    • Solution for Problem #9
    • Lecture 20 :
    • Problem #10
      • Pove that: (AB)^2 <= (A^2)(B^2)
    • Lecture 21 :
    • Solution for Problem #10

  • Section 6 : Practice The Advanced Topics 21 Lectures 00:46:53

    • Lecture 1 :
    • Section Preview
    • Lecture 2 :
    • Warm up Problem
      • Prove: (A x B ) = - B x A A,B are vectors
    • Lecture 3 :
    • Solution for The Warm up
    • Lecture 4 :
    • Problem #2
      • Prove: (A x B ) (C x D) = (AC)(BD) - (AD)(BC) A,B,C,D are vectors
    • Lecture 5 :
    • Solution for Problem #2
    • Lecture 6 :
    • Solution for Problem #3
    • Lecture 7 :
    • Solution for Problem #4
    • Lecture 8 :
    • Solution for Problem #5
    • Lecture 9 :
    • Solution for Problem #6
    • Lecture 10 :
    • Solution for Problem #7
    • Lecture 11 :
    • Solution for Problem #8
    • Lecture 12 :
    • Solution for Problem #9
    • Lecture 13 :
    • Solution for Problem #10
    • Lecture 14 :
    • Problem #3
      • Prove the identity: A  x ( B x C ) + B  x ( C x A ) + C  x ( A x B ) = 0 A ,B ,C are vectors
    • Lecture 15 :
    • Problem #4
      • Prove: ∇(ψφ) = ψ∇φ + φ∇ψ where ψ, φ are scalar functions
    • Lecture 16 :
    • Problem #5
      • Prove: ∇(ψA) = ψ∇A + A • (∇ψ) where: A is a vector and and ψ is a scalar function
    • Lecture 17 :
    • Problem #6
      • Prove: ∇ × (ψA) = ψ(∇ × A) + A × (∇ψ) where A is a vector and ψ is a scalar function
    • Lecture 18 :
    • Problem #7
      • Prove: ∇( A × B ) = B • (∇ × A) − A • (∇ × B ) where A,B are vectors
    • Lecture 19 :
    • Problem #8
      • Prove: A x ( B x C ) = ( A · C )B - ( A · B) C where A,B are vectors
    • Lecture 20 :
    • Problem #9
      • Prove: ∇ × ( A × B ) = (B · ∇) A + (∇ · B) A − (∇ · A) B − (A · ∇) B where A,B are vectors
    • Lecture 21 :
    • Problem #10
      • Prove: A · A x B = 0 where A,B are vectors

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Instructor

Salih Zinaty,

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Zinaty is a Senior Electrical and computer engineer worked in wide range of positions: • System performance analyst. • Software Project manager. • Back End Developer. This unique career path equipped him with a various skills: • high mathematics skills. • system engineering. • Project management. • Back End developing: node.js, java, python. • Self learning skills. In order to gain more profound knowledge in his career, he studied the core courses of the physics major witch introduced him to new mathematical and physics concepts. The main core for engineering is without a doubt is mathematics and physics. Therefore, in order to develop new technologies and make the world a better place, knowing the core concepts are a must. Developing and learning new leading technologies is his truly passion. However, he believe that in order to become a better developer in the High-Tech fields, knowing mathematics and physics is a critical advantage. He believe that the right way to grasp a concept in the different scince fields, is to practice it. His courses will give the true opportunity to learn the theory and practice it in the most efficient way.
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