- PREFACE: TO STUDENTS

What This Book is About | How to Use this Book


What This Book is About [ Top ]

This book is written to help you understand the inner workings of how things change and to help you build systematic ways to use this understanding in everyday real-life situations that involve change. Indeed, a primary focus of the material is on change, since calculus is the mathematics of change.

Even if you have studied calculus before, this book is probably different from any other mathematics textbook that you have used. It is based on three premises:

  1. Understanding is as important as the mastery of mathematical manipulations. Algebraic skill and the skill to manipulate expressions must be regularly practiced, or they will fade away. If you understand concepts, you will be able to explain some things in your life forever.
  2. Mathematics is present in all sorts of real-life situations. It is not just an abstract subject in textbooks. In real life, mathematics is often messy and not at all like the tidy, neat equations that you were taught to factor and solve. Speaking of equations, where do they come from? Nature seldom whispers an equation into our ears.
  3. The new graphics technology in today's calculators and computers is a powerful tool that can help you understand important mathematical connections. Like many tools in various fields, technology frees you from tedious, unproductive work; enables you to engage situations more realistically; and lets you focus on what you do bestů think and reason.


How to Use this Book [ Top ]

  • Begin by throwing away any preconceived notions that you may have about what calculus is and any notion that you are "not good" in mathematics.
  • Make a commitment to learn the material; not just a good intention, but a genuine commitment.
  • Study this book. Notice we've said "study", not "read". Reading is a part of study, but study involves much more. You should not only read (and re-read) the discussions, but work through each example to understand its development.
  • Use paper, pencil and your graphing calculator or computer when you study. These are your basic tools and you cannot study effectively without them.
  • Find a study partner, if at all possible. Each of you will be able to help the other learn. Communicating within mathematics, and about mathematics, is important to your overall development toward understanding mathematics.
  • Write your solutions clearly and legibly, being certain to interpret all of your answers with complete sentences using proper grammar. Careful writing will help you sort through your ideas and focus your learning.
  • Make every effort not to fall behind. You know the dangers, of course, but we remind you nevertheless.
  • Finally, remember that there is no substitute for effective study. You have your most valuable resource with you at all times&emdash;your mind. Use it.





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