If you would like to study antennas, you might like to try EZNEC.
This program is available in a free version, which has some limits, but the program is still amazing.
www.eznec.com
Look for the DEMO version.
This program has a deceptively simple main screen in a small window, but persist for a while and you will see why this is an extremely popular program.
It works on a system of WIRES which can be actual wires or they might be pipes or large pieces of metal.
You just tell it where these wires are in space and where you would like to feed one or more of the wires with radio frequency power and it works out the resulting transmit pattern. You don't have to give it any maths as it can work all that out by itself.
The radiation pattern can be vertical, azimuth (horizontal) or 3D.
You can get resonance information by using the SWR (standing wave ratio) graphing.
It divides the wires up into segments. The center of a segment is regarded as the radiating point for the whole length of the segment. It is also a possible feed point.
The free version allows you 20 segments.
This is plenty for simple antennas, but limiting for complex systems.
The commercial versions allow you hundreds of segments, but you have to pay for those. Definitely worth it if you get serious about antennas.
