What book is good in studying beginning optimization?

A very good Introductory book with detailed explanation

http://www.amazon.co.uk/Linear-Nonlinear-Optimization-Igor-Griva/dp/0898716616

The tip I would give is just like all the other maths please practice and write detailed solution. In Optimization solutions can be very very long but i highly recommend solving them.

Also one often forgets the algorithm if not using every day so write a summary for list of methods you use and how to use them for quick reference.

Numerical Optimization by Nocedal and Wright is quite a classic in the field. It also contains a few appendices introducing an overview of the necessary background.

I learned it from Mathematical Modeling by M. Meerschaert.

The problems allow for interesting questions that go beyond his suggested exercises, so it's a great source of problems. Also, he writes problems that give you an excuse to learn things like Maple or R

Regarding what Calculus to review for this text, you should learn about Newton's Method, the gradient operator, the Jacobian matrix, and Lagrange multipliers. Khan Academy has videos on some or all of those topics.