This book endeavors to achieve a healthy balance between the presentation of elementary calculus from a rigorous approach and that from the intuitive and computational point of view.
An excellent book; if you want to know whether or not something is true, it'll be in this book. But be warned: the author discusses every subject in the utmost generality. There's a time for rigor, and a time for intuition.
A great calculus textbook. No glossy pages or color pictures, but Leithold goes through each procedure in a thorough way proving each theorem as they are introduced. The reader needs a strong understanding of algebra before undertaking this material.