General aviation pilot reported a near miss with an aircraft landing opposite direction at a non-towered airport. The pilot took evasive action to avoid a collision.

Narrative

There were 3 aircraft in the pattern actively making calls on the CTAF at WDR. Winds were calm. When we entered the pattern; Runway 13 was in use per calls on CTAF. At approximately XA:40 I had just taken off and was on the upwind of Runway 13 and observed a fast moving aircraft on the approach to land on Runway 31. There had been no calls on the CTAF; and evasive action was taken to move right and increase rate of climb to ensure avoidance. My instructor made a call to warn the aircraft who had just radioed he was taking the runway to takeoff on 13 so he was aware of the landing traffic; and asked if the aircraft landing on the opposite runway was on frequency. There was a response of 'yes; on short final for 31.' My instructor alerted the pilot that there were multiple people in the pattern and 13 was currently the active runway. There were no further communications from the pilot until he radioed he was exiting the runway to the taxiway. We noted that this aircraft not making calls and landing opposite other traffic.