L5 Vectors & Coordinate Systems

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This is basically a short math review chapter. If you have trouble with these vector problems, please review yourself.

⚿1: Vectors vs. Scalars vs Tensors

• Scalars have a magnitude. They are a single number: Temperature (T), Volume (V), Mass (m), Pressure (P). They are a rank-0 tensor. They may be specified as a
• Vectors have a magnitude + direction. To specify a vector in three dimensions you need three numbers. They are a rank-1 tensor. Each component may be specified as a_i
• A rank-2 tensor looks like a 3x3 matrix. (we will not discuss but they are very important) Each component may be specified as a_ij

⚿2: 3D Coordinate systems

To specify a position in space and time we need 4 numbers. For example, (x,y,z,t) or (r,z,φ,t) or (r,θ,φ,t)

Today's Lecture: Knight Chapter 3 Lecture Slides