The Kli Yakar explains: Yitschak blessed Aisov and said that should Yaakov not toil in Torah then Aisov shall have the reigns over Yaakov.
Aisov knew that in aveilut, Yaakov would not toil in his learning,since leHalacha an avel may not toil in learning being that Torah brings happiness to a person and therefore he shall seize the opportunity to have the upper hand over Yaakov and kill him.
I would like to add another explanation.
The Yaaros Devash in Derush 7' in the paragraph beginning with 'אבל דע כי מיתת הצדיק היא לתשובה' says that upon the death of a Tsaddik who his lifelong goal was to bring people up in their Avodat Hashem,the Tsaddik himself shall come down and bring the people strength to overcome their Yetser Ho'Rah.He will plant a new heart in them, a heart which longs to serve Hashem.
However, says the Yaaros Devash, in order for the Tsaddik to connect to you and thereby lift you, you shall need to start longing to do good on your own and then he shall gain permission to intercede on your behalf and be granted the power to lift you up with him.
How will that happen: By being Maspid (eulogizing) the Tsaddik, you are inspired to Teshuvah and to follow in his ways. In other words by crying over the Tsaddik you shall come to Teshuvah.
Now, according to the words of the Yaros Devash,i would like to explain; Aisov, with his will do rid himself of Yaakov,feared sitting Shivaah and crying after his father, knowing that he just might come to teshuva and be elevated to great heights and then killing Yaakov or anyone else for that matter will certainly be out of the picture.
Therefore he shall use the tactic of 'out of sight, out of mind' and ignoring the entire mourning he shall immediately turn to his goal, and kill Yaakov before anything good shall inspire him to Teshuvah.
In short aveilut was purposefully as any other day fearing that it will have an affect on him and he won't want to carry out his plan anymore.