If you just want to get the DayOfWeek in your computer, you have two simple solutions. The first one is to get it directly from the first word of your %date% variable "Tue 08/18/2015" :):
for /F %%a in ("%date%") do set dow=%%a
But if you want to perform the numeric calculation, you may use the method to convert a date into the Julian Day Number shown at this answer:
@echo off
setlocal
rem Modify next line accordingly to your locale format (this one use "Dow MM/DD/YYYY")
for /F "tokens=2-4 delims=/ " %%a in ("%date%") do set /A mm=1%%a-100, dd=1%%b-100, yyyy=%%c
rem Convert the Date to Julian Day Number, and get its Day Of Week (0=Sunday, ..., 6=Saturday)
set /A a=(mm-14)/12, jdn=(1461*(yyyy+4800+a))/4+(367*(mm-2-12*a))/12-(3*((yyyy+4900+a)/100))/4+dd-32075, dow=(jdn+1)%%7
rem Show the result
echo Day of week: %dow%
The set command use the trick explained in other answers in order to correctly get numbers greater than 07 that start with zero. For example, if the mont is 08, then set /A mm=1%%a-100 is set /A mm=108-100, that gives 8.
However, if you want to use this method on different computers, that may have different locale date formats, then you must use the method suggested by foxidrive.