Week 1:

Take the quiz by 6:00 pm Wednesday.

This week we will review vectors and vector calculus. If time allows we will begin a review of electrostatics.

Vector

• Standard definition: Magnitude and direction.
• More abstract: Transformation properties under rotation.

All theories require a set of assumptions from which all ramifications of the theory are derived. We search for the most fundamental basic ideas as our starting point. Key theories in particle physics view natural symmetries as very fundamental principles. Space is isotropic is one such statement of symmetry. Another way of stating this principle is to say that the laws of physics should not change under rotation and/or translation (transformations). Definitions that describe an entity by its transformation properties are therefore very important.

• Vector components (cartesian, spherical, cyclindrical) operations, identities
• Vector calculus.

• relationship between differential and integral formulas.
• divergence theorem
• Stoke's theorem

This mathematics will then be applied to help us understand the behavior of fields that are constrained by Maxwell's equations.

The divergence tells us that quantities that have a source (light from a bulb) can only be created or lost at sources and/or sinks. An intuitive example is fluid flow. A source of water, a faucet, will cause water to flow. Water will flow through all kinds of systems but all those systems will satisfy the rule the rule that water that goes into a volume will leave the volume or accumulate (sink). Of course if the volume contains a source of water then the amount out will be greater by the strength of the source.

The curl describes another method to make water flow. This method doesn't require a source but something to stir the water.

It turns out that the flow of a fluid can be completely determined by finding all the sources and sinks, adding all the elements that are stirring the fluid and by the flow of the fluid at the boundaries. This is what Maxwell set out to do. And he succeeded.

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