Calculus is a very important subject. It is the mathematical language needed to study change; wherever in science there are quantities that depend continuously on time and location, calculus is the appropriate tool. The basic laws of all branches of science which deal with changing quantities are expressed using calculus. Only with a knowledge of calculus can you approach the study of these subjects.

Given the importance of the calculus, it is a good idea to learn it well. You need a usable knowledge of subject, so if you just do enough to squeak through the course, you are really wasting your time.

The first thing to think about is how much time you need to budget for this course. I would say upwards of eight to ten hours per week, exclusive of exam preparation time.

Here is some advice about what you need to do:

1. You need a good working knowledge of your previous mathematics courses in algebra, geometry, and elementary functions (including logarithms, exponential, and trigonometric functions).} This does not mean that you have to remember every detail today. It does mean, however, that you need to be comfortably familiar with the ideas, and reliable in doing algebraic computations by hand.

Moreover, you need to take responsibility to identify weak spots and to review previous work as needed. When you make an algebra mistake, indeed, when you make any mistake in your work, you need to treat that not as a randomly occurring natural misfortune, to be borne passively, but rather as a clue to something you don't understand, to be tracked down, uncovered and corrected; your mistakes are opportunities to learn.

2. You need to spend a minimum of eight to ten hours per week outside of class in thoughtful concentrated effort studying calculus. The best students will need to spend this time to achieve the thorough knowledge of calculus which will be useful in future work. The weakest students will need this time and more merely to survive.

3. You need to read your text. You need to know what is in the text. The lectures and recitation sections will not precisely repeat the material in the text, but complement it, provide insights into the material and practice with using it. Reading the text does not mean briefly skimming through it, but actively studying it.

You must not skip the examples in the text, which are essential both for understanding the material and for completing the homework; you will have adequately understood an example when you can close the text and reproduce the example on paper.

4. You need to attend the lectures and recitation sections. Something important will be done in every class, and you will be expected to know about it. You should be prepared to take an active part in class, to ask questions as necessary, and to do practice exercises given to you in class. You will need to take notes on the lectures and to review your notes actively; sometimes the structure and purpose of the lecture will become clear to you only when you study your notes after class.

5. You need to do the homework completely and thoughtfully. I haven't yet met someone who could learn calculus without doing plenty of homework. Bearing in mind that the homework is for you, not for me, you should carry on a dialogue with yourself about it: What did I learn in this problem? What did I practice? What techniques did I use? Can I outline the steps which I needed to do this? Were there any unexpected turns in the problem? Did I make any mistakes which reveal a need for some more practice? etc. etc.

I will assign what seems to me a reasonable amount of homework. Perhaps you will need to do more in order to instruct yourself adequately. Take responsibility to do what you need to do.

6. You need to do some memorization. There are certain concepts, definitions, and theorems which are so fundamental that you should know the precise formulation. Often memorization is the first step towards real understanding of the concepts (which is of course the ideal goal). I will point out material which you need to memorize, and will give you some hints about how to go about it.

7. You need to allow adequate time to review for quizzes and exams and to review actively and intelligently. It is unlikely that a couple of hours at the last minute will suffice. We will discuss exam preparation in class at the appropriate time. Exam preparation is a time for you to construct an intellectual synthesis of the course, to put your knowledge in order. It is for this reason that exams can be a useful learning experience.

8. You need to take advantage of help which is available to you. The university provides a free mathematics tutorial laboratory, where you can study, get help from knowledgeable teaching assistants, sign up for extra help with difficult topics, and use computer-instruction aids.

9. You need to have, or to develop, patience, persistence, and intellectual courage. Mathematics has certain virtues to teach, and the acquisition of these virtues is more important for learning mathematics (and for living) than any particular technique which you might learn. The most important thing to be learned in this course is to face a problem for which it is not all apparent at first what method or technique might be useful, and to discover, by patient involvement with the problem, what is to be done.

10. Above all, you need to take responsibility for your learning. All that I can do is explain, assign reading and practice exercises, answer questions, offer encouragement, and guide you to helpful resources. But you have to do the learning.

Some students may think that mathematics is supposed to be ``made" easy, and if it is not so, then something is wrong with the subject, the teacher, or the textbook. Calculus will be easy once you have learned it, not before. Learning mathematics is not easy, but it can be accomplished by persistent and intelligent effort.