Hello, first you may be asking why go Warwick top and why AP on Warwick. Welp, continue reading if you want to know. :)

Hungering Strike - The bread and butter of AP Warwick, lets break this skill down.

1:1 AP ratio: having 600 AP gives it additional 600 damage on your Q, simple.
16% maximum health damage... Whoa... 16% max health late game is huge plus adding AP ratio makes this a huge nuking ability.
80% healing- simple 80% of damage dealt is healed, this gives huge dueling potential and lane sustain.
6 second cool down becomes 3.6 after 40 % cdr, very low for a very good ratio.

Pros

Very good laning phase
Good trade/poke
High sustain
Good roam

Cons

Mana dependent
Ult is only cc

Nashor's Tooth
This item fits AP Warwick perfectly, the 20% cdr plus the Unique Passive.
The passive gives every AA 15 + 15% AP.
Warwick's ultimate procs on hit effects 5 times.

So 15% X 5 = 75% ap ratio on ultimate + 75 flat from passive.

This item plus DFG leads for a hard hitting Infinite Duress

Boots

Sorceror's Shoes
This is the most preferred boots as the magic pen works well.
Ionian Boots of Lucidity not needed as you have max CDR
Boots of Swiftness Don't need since you have much gained movement speed from Blood Scent

Warwick excels at many matchup as AP, except when they do counter him it hurts alot.
Best matchups are usually against champions with low sustain and squishiness.
Yasuo Pantheon Nasus
Bad matchups are usually against ranged or tank champions. As Warwick pre-6 has a short range.
Malphite Jinx Quinn

In lane always use your Q when ever possible. Warwick doesn't have much all in potential until level 6 and 2/3 items. You will pretty much always win trades as your q heals and deals tons of damage.
Remember to farm since you are somewhat item dependent, and don't be afraid to enter an empty lane with 100 hp as one q heals around 15% of your hp ish.

After laning phase you want to mainly focus squishes and catch people off gaurd.
In team fights use this Combo

Deathfire Grasp--> Infinite Duress While in Ultimate Ignite
ending up with a finishing Hungering Strike