Have you taken calculus?

In understanding the derivations, a strong calculus background is desirable. You should also be familiar with multivariable calculus because partial differentiation is useful when studying the wave nature of particles; differential equations when studying Schrodinger,etc...

The text book I used wasPhysics for Scientist and Engineers with Modern Physics, 7Eby Raymond Serway and John Jewett, Jr. Chapters 39-46 deal with quantum mechanics and modern physics. It's a great text.

Another good text in understanding Quantum mechanics on a more advanced mathematical level would beQuantum mechanics : a conceptual approachby Hendrik Hameka.

Also, I would suggest readingIn Search of Schrodinger's Catby John Gribbin. This book is great for those who want to know more about the history and progress of quantum mechanics.