## Topics for Midterm Exam 1

COMPLEX NUMBERS

complex conjugate (rect and polar form)
reciprocal (rect and polar form)
don't get mixed up with vectors
remember to invert complex impedance in parallel

VECTOR ALGEBRA

dot product (ab\cos\theta and sum of products of components)
cross product (direction, magnitude, Cartesian components,
BAC-CAB rule

COORDINATE SYSTEMS

cylindrical
spherical polar

DERIVATIVES

sin and cos
e^{j\phi}
powers

TRIG FUNCTION VALUES

sin, cos and tan at 0, \pi/2 and \pi
units of \phi in e^{j\phi} (\pi not needed!)

EMAG CONCEPTS

Electric field of a point charge
interpretation of direction and magnitude

Gauss' Law
use integral form to get D in planar, cylindrical
and spherical geometries
differential form

Electrostatic potential
differential and integral relations between \Phi and E
Poisson's equation
Laplace's equation

Field lines and equipotentials

Boundary conditions on D_n

Boundary conditions on E_t

Calculate capacitance using D and E fields

Superposition principle (vector!)

Current densities
surface
volume

VECTOR CALCULUS

gradient of a scalar field
Cartesian
cylindrical
divergence of a vector field
Cartesian
cylindrical
remember to multiply
F_\rho by \rho, then take derivative

line integral (don't confuse with volume or surface integral)

curl of a vector field
Cartesian
cylindrical

Stokes' theorem

know which operators operate on scalar fields
know which operators operate on vector fields
know which operators produce scalar fields
know which operators produce vector fields