Hello, I am a recent high school graduate and I have recently finished calculus II with one year of calculus I prior (which I took junior year). My major will be physics at the University of Texas and having told that I completed those courses to my advisor he said I seemed bright from the conversations we had and wouldn't mind placing me in multivariable calculus. It is now summer and I have decided to study the course ahead. I looked for a PDF of Apostol's but I found it very rigorous in its presentation. I easily grasp concepts and methods and I can usually undertake difficult problems but some of the problems were extremely difficult in the sense that if you read the chapters and understood as far as the text goes, the problems seemed still too hard. So as for my questions: 1. should I study Spivak before Apostol? 2. What kind of mathematical background would one require to master Apostol? And 3. What is meant by "mastering" a textbook? To study as I plan to, is it a good idea to try to do every single problem or just conceptual/exploratory problems with some mechanical (to get used to the mechanics of problem solving) problems?