You may need to consider a better backup plan, unless you don't mind loosing data.
First and foremost, make sure you use a COPY of you backup from Sunday in case something goes wrong during recovery.
You can recover from Sunday's backup, but you'll have to recreate the controlfile from scratch if you don't have a backup of one and then recreate the controlfile once you have the database in NOMOUNT mode.
Within SQLPlus, you can run the following:
STARTUP NOMOUNT;
-- Sample create controlfile command
-- you'll need to modify to your environment
CREATE CONTROLFILE REUSE DATABASE "<DBSID>" RESETLOGS
MAXLOGFILES 32
MAXLOGMEMBERS 2
MAXDATAFILES 254
MAXINSTANCES 1
MAXLOGHISTORY 449
LOGFILE
GROUP 1 '/oracle/oradata/database/redo01.ora' SIZE 1M,
GROUP 2 '/oracle/oradata/database/redo02.ora' SIZE 1M
DATAFILE
'/oracle/oradata/database/system01.ora' SIZE 100M,
'/oracle/oradata/database/rbs01.ora' SIZE 40M,
'/oracle/oradata/database/user01.ora' SIZE 25M,
'/oracle/oradata/database/indx01.ora' SIZE 25M,
'/oracle/oradata/database/tools01.ora' SIZE 10M;
ALTER DATABASE OPEN RESETLOGS;