Singleness of heart

Today after several hours of studying calculus I was feeling particularily discouraged and decided to go for a walk outside. The sky was misty and gray and I borrowed a jacket from my brother and wove my way into the back 40 and down the muddy trails. I poured my heart out to God about all the things that were bothering me, how much I wanted to get close to him, how much I loved him.
I finally stopped under a sweeping moss-covered tree, on a decrepit old red bridge that was suspended over a muddy creek. On the banks of the river bright yellow skunk cabbage flowers were poking out of the dark earth. It had stopped raining and suddenly as I stood there against the railing, the sun came out from behind the clouds and flooded the whole little valley with warm sunshine. It was so beautiful, my words couldn't ever do it justice.
I asked the Lord, how can I love you with all my heart but still be passionate about other things? Psalm 86 says "teach me your way, O Lord, and I will walk in your truth. Give me an UNDIVIDED heart, that I may fear your name. I will praise you, O Lord my God, with ALL my heart; I will glorify your name forever."
But even I can read the tension in these verses. David was a married man. He was king of a nation. His interests were divided. How could ALL of his heart be praising God when a good part of it must have been occupied with the practical concerns of life?
I feel discouraged because I want all of my heart to be completely for the Lord all the time, but it isn't. When I try to fast and pray all I think about is food. If I think about devoting my life to the mission field and staying single, all I want to do is get married. When I try to pray my mind wanders. I enjoy my studies so much and I love spending time with friends.
How can my heart be undivided towards the Lord?
As I walked away from the river, the sun filtering through the trees and making everything sing, I felt this overwhelming sense of God's love. It is so amazing, I think, that even though I try and try but never manage to love him completely, he still loves me! He love me completely! He loves me all the time!