Advanced calculus : theory and practice - Petrovic, John Srdjan (Textbooks in mathematics)
"This textbook strengthens students' computational skills, teaches them how to prove theorems, and helps them understand proofs. Designed for junior and senior undergraduates, the book includes historical background for many concepts and theorems. It begins with the calculus of one variable and progresses to multivariable calculus in the second half of the book. An introductory section in each chapter reviews the material covered in earlier calculus courses, easing students into the more serious material. A solutions manual is available with qualifying course adoption"--