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Vectors | Lecture 1 | Vector Calculus for Engineers
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Vectors | Lecture 1 | Vector Calculus for Engineers

Introduction to Vector Calculus

In this section, the concept of a vector is introduced and its properties are discussed.

Vectors and Scalars

  • A vector has a length and direction.
  • Scalars only have length.
  • Examples of vectors include acceleration and electric field, while examples of scalars include mass and electric charge.

Algebraic Properties of Vectors

  • Vectors satisfy commutative, associative, and distributive laws.
  • Scalar multiplication changes the length but not the direction of a vector.

Adding and Subtracting Vectors

This section covers how to add and subtract vectors.

Adding Vectors

  • To add two vectors, place them head to tail.
  • The resulting vector goes from the tail of the first vector to the head of the second vector.

Subtracting Vectors

  • To subtract one vector from another, flip the direction of the negative vector and add it to the other vector.
  • The resulting vector goes from the head of the first vector to the head of the second vector.
Video description

Defines vectors, vector addition and vector subtraction. Join me on Coursera: https://imp.i384100.net/mathematics-for-engineers Lecture notes at http://www.math.ust.hk/~machas/vector-calculus-for-engineers.pdf Paperback at https://www.amazon.com/Vector-Calculus-Engineers-Mathematics/dp/B0BMJMRYBH/ Subscribe to my channel: http://www.youtube.com/user/jchasnov?sub_confirmation=1