1. Chapter 3 Overview

2. Laws of Vector Algebra

3. Properties of Vector Operations
Equality of Two Vectors
Commutative property

4. Position & Distance Vectors
Position Vector: From origin to point P
Distance Vector: Between two points

5. Vector Multiplication: Scalar Product or ”Dot Product”
Hence:

6. Vector Multiplication: Vector Product or ”Cross Product”

8. Triple Products
Scalar Triple Product
Vector Triple Product
Hence:

9. Cartesian Coordinate System
Differential length vector
Differential area vectors

11. Cylindrical Coordinate System

12. Cylindrical Coordinate System

15. Spherical Coordinate System

17. Coordinate Transformations: Coordinates
To solve a problem, we select the coordinate system that best fits its geometry
Sometimes we need to transform between coordinate systems

18. Coordinate Transformations: Unit Vectors

20. Distance Between 2 Points

21. Gradient of A Scalar Field

22. Gradient ( cont.)

23. Divergence of a Vector Field

24. Divergence Theorem
Useful tool for converting integration over a volume to one over the surface enclosing that volume, and vice versa

26. Curl of a Vector Field

27. Stokes’s Theorem

28. Laplacian Operator Laplacian of a Scalar Field
Laplacian of a Vector Field
Useful Relation