trig
functions 
 basic properties of sin,
cos, tan, ...
 relationship between degrees and radians (180deg = pi
radians)
 geometrical interpretation (e.g., cosine =
adjacent/hypotenuse)
 relationships: sin^{2} +
cos^{2} =
1, tan(a)
= sin(a)/cos(a), etc.

exponentials
&
logarithms

 basic properties of exponentials, e^{0} = 1, e^{1} ~ 2.71818, etc.
 sketch exponential decay curve, exponential charging curve
 graphically identify time constant, 1/e ~ 37%
 identify time constant from equation
 properties of logs, log(0) = infinity, log(1) = 0, ln(e)
= 1, etc.
 choice of base10, base2, natural log, etc.
 convert from one base to another
 semilog, loglog plots

derivatives 

integrals


vectors
&
matrices


ordinary
differential
equations

 differential equations as models
 temporal derivatives as rateofchange
 ability to integrate simple cases by hand
 numerical integration, Euler's method
 initial value specification (where to start)
 steadystate solutions
Euler's
Method

basic
electrical
circuit
analysis

 Kirchoff's current law (current conseration at nodes)
 Kirchoff's voltage law (sum of voltage drops around a loop
is zero)
 Ohm's law: V = I R
 Conductance is inverse resistance g = 1/R; Ohm's law: I = gV
 Capacitance: q = CV
 Capacitive current: I =
dq/dt
= C dV/dt
 RC circuit, RC time constant
Analysis
of Resistive Circuits
