Pre-requisites
Calculus
- Vectors, dot product, cross product, scalars vs vectors, meaning of parallel as $\myv a \parallel \myv b \leftrightarrow \myv b=c\myv a$.
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(know and apply thoroughly) derivatives and integrals of power functions, $x^p$ (where $p$ is positive or negative), and elementary function like $\sin, \cos, e^{ax}, e{iax}, \ln$.
- Geometric interpretations: $y'$ as slope, $y''$ as curvature, $\int_a^b f(x)\,dx$ as an area.
- (know and apply thoroughly) the product rule, the chain rule
- Complex arithmetic and algebra: z=X + iY and graphing in the complex plane. Euler relation $e^{i\theta}=\cos\theta + i\sin\theta$.
- (know and apply thoroughly) coordinate systems: 2-d--Cartesian and polar and complex plane. 3-d-- Cartesian, cylindrical, spherical-polar
- Complex arithmetic and algebra:
- Integration in 3-d
- Potential functions... path independence, curl test, guessing-and-checking a potential function. Integrating a conservative vector field to find the potential function.
- Taylor expansions
General Physics
- $\myv F=m\myv a$, linear and angular momentum conservation, energy conservation (in the absence of friction. Energy conservation with friction (if you account for heat).
Centripetal acceleration, circular motion where $v/r=\omega$, relationships between $\omega$, period and frequency.
- Approach of finding derivatives through $\lim_{\Delta t\to 0}\frac{\Delta f}{\Delta t}=\frac{df}{dt}\equiv \dot f.$
- Inverse square laws for gravity, electric force. Lorentz force of ...
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