This book presents Newtonian mechanics in all its theoretical "math nerd" glory. All necessary mathematical topics are covered with "physics rigor" that allows you to gain a usable knowledge of the mathematics in a minimal time. It has been the only book I've found that sticks to Newtonian mechanics, yet avoids the point and click "apply equation X here" methods that most introductory University texts give. I used it as a supplement to my assigned physics book for Mechanics and Heat and felt exceedingly more prepared than my fellow students with each succeeding chapter.
If you're a motivated student, I highly suggest picking up this book. The first year or two of a University Physics program can be uncomfortably dry and you'll hear many times that students don't feel like they're doing "real" physics until their Junior year. This book will allow you the feel of doing "real physics" while sticking to the Newtonian mechanics that you'll use for your courses. By the end of the book, you'll feel comfortable with all the mathematical derivations and applications of Newtonian mechanics, have a solid grasp of harmonic oscillations, have a solid background in solving ordinary differential equations, feel comfortable with matrix algebra applications, and get the enjoyment that comes with doing "real physics" a good year or two before your classmates.
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