### PH 422 Math Bits

##### Divergence (40 min)
• Definition of divergence (Lecture) 20 min
• Visualizing Divergence (Maple Visualization) 20 min Students practice estimating divergence from graphs of various vector fields.
##### Divergence Theorem (20 min)
• Reading: GVC § Divergence Theorem
• Derivation of the Divergence Theorem (lecture). We follow “div, grad, curl and all that”, by Schey. The Divergence theorem is almost a lemma based on the definition of divergence. Draw a diagram of an arbitrary volume divided into lots of little cubes. Calculate the sum of all the fluxes out of all the little cubes (isn't this a strange sum to consider!!) and argue that the flux out of one cube is the flux into the adjacent cube unless the cube is on the boundary.
##### Stokes' Theorem
• Reading: GVC § Stokes' Theorem
• Derivation of Stokes' Theorem (lecture). We follow “div, grad, curl and all that”, by Schey

### PH 425 Math Bits

#### Unit: Operators and Transformations in Linear Systems

##### Inner Products and Norms
• Calculating Inner Products and Normalization of Vectors (Lecture, ?? minutes)

Write these lecture notes. Emphasize complex vectors.

### PH 423 Math Bits

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