Preface to the Student

Welcome

Welcome to Calculus! This text covers a single-semester college-level course in Differential Calculus (which your college probably calls Calculus I). While I could wax poetic about the beauty of this subject, I really should focus on getting you the knowledge you need to start this course off on a good foot.

The Need to Read

It's no secret that many students make it through Algebra without cracking open their textbook, and some even manage to pass Precalculus or College Algebra using the same technique. Calculus, on the other hand, is a completely different beast. You will need to take advantage of every resource available to wrap your mind around the concepts of this course. Foremost among those resources is this textbook! Do not expect to read it like a book and devour 40 pages in an evening's study session. This material is dense and requires contemplation. Expect to read paragraphs several times before being able to completely understand what's going on. This "constructive struggle" is beneficial in the long run - trust me.

Horse... THEN Cart

Many students try their hand at the homework and only reference the text when they are completely befuddled. This is known as "placing the cart before the horse." If you think of the "cart" as the knowledge you need to attain in the section and the "horse" as the knowledge you currently have, then your initial situation in any section is a cart-load of information you need to figure out, and a small horse (your current understanding of the material in the current section) to pull that cart. With this poorly-designed analogy in mind, the order in which you should do things in a calculus course is as follows:

1. Grease the Wheels: Perform a cursory read-through of the section before attending the lecture. Don't expect to understand everything, but try your best to get a conceptual understanding of the goal of the section. Doing this cursory read-through is "greasing the wheels" to make the classroom experience much more enjoyable (yes, I said it!) and understandable. It also moves a small amount of that cart of unattained knowledge to the horse (making the horse a bit stronger and the cart a bit lighter).
2. Push-Start the Cart: Attend the lecture and ask questions as your professor gets to moments that confused you. The lecture should "push the cart" to help you get the momentum so you can start really learning the topic. During this phase, your professor is helping you lighten the load off your unattained knowledge cart and, simultaneously, making your horse stronger (filling in your knowledge gaps).
3. Use the Momentum to Move Forward: After lecture, thoroughly read the section, taking notes as you do so. You should not do this in a single sitting. Rather, dedicate an hour or so to reading the text and taking notes, give yourself a break, study another subject or go to work, then come back to the textbook and spend another hour reading and taking notes. Repeat this process for a couple of days until you have successfully finished the section. Make sure you try the Examples in the text prior to reading the worked-out solutions. During this step, the amount of unattained knowledge should dwindle to very little and your actual knowledge of the material in the section should grow.
4. Let the Horse Pull the Cart: Once you have greased the wheels, push-start the cart, and used the momentum to move forward, you THEN let the horse do all the work. That is, you let your knowledge carry you into the homework.