Spring 2008

Professor C. D. Cantrell, UT-Dallas

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