1. 1. Vector Analysis 1.1 Vector Algebra

2. 1.1.1 Vector operations A scalar has a magnitude (mass, time, temperature, charge). A vector has a magnitude (its length) and a direction. Examples: velocity, force, momentum, field strength. Boldface letters denote vectors. On the blackboard I use. Unit vectors are denoted by

3. Vectors have no location. -A Vector field A(r)

4. addition of two vectors: A+B multiplication by a scalar: aA

5. dot product (scalar, inner): if parallel if perpendicular Example work

6. Example 1.1

7. cross product (vector, outer): is the unit vector perpendicular to the AB-plane. form a right-handed system. is the area of the parallelogram. Example: angular momentum

8. 1.1.2 Component Form 1: x, 2: y, 3: z components: basis:

9. common notation: Kronecker symbol Properties of the basis

10. Levi-Civita symbol

11. Example 1.2

12. 1.1.3 Triple Products scalar triple product: volume

13. vector triple product: bac - cab rule Higher order products by repeated bac-cab and symmetries of the scalar triple product.

14. 1.1.4 Notation

15. 1.1.5 How Vectors Transform Rotation about the x-axis: In general