Applied Mathematics 2277A/B Final: Final Studying Ch 15
5 May 2019
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Def: every point in space has a vector associated with it. Introduction to vector manipulation (div, grad and curl) So, we can associate potential energy with a vector field (like a potential energy increases as you get further from the origin). Def: if there is a vector field where potential energy is conservative, that is a conservative vector field. Conditions to satisfy for a vector field to be conservative. 1. if there exists some scalar field ( ) such that f = , then f is a conservative vector field. This is checking whether the field has an equipotential surface. It"s a constant which practically represents the equipotential lines associated with the potential energy in the vector field. Then field series (which i don"t get but it"s probably fine) And he skipped sources, sinks and dipoles b/c they are just other properties of the field. Def: a line integral is an integral where the axis of integration is a curve.
