Although this material can be used with any book or books covering the three title subjects, it is being written together with the textbook Multivariable Calculus, Linear Algebra, and Differential Equations in a Real and Complex World. Textbooks and Web-based material like this complement each other, each has strengths and weaknesses and by using both together we get the advantages of each.
Learning mathematics is above all an active pursuit -- the only way to learn mathematics is by doing mathematics and the only way to learn how to use mathematics to solve real problems is by using mathematics to solve real problems. This package -- the book and the Web -- are designed for active learning. The Web, in particular, provides a wonderful medium for active learning. As you work with this material you should have both a browser window (this window) and a CAS window (Maple, Mathematica, or the TI-92) open, side-by-side on your screen, and you should go back-and-forth between the two -- reading, looking, and listening in your browser window -- and doing and using mathematics in your CAS window. In addition, many modules have a "hands-on" component, using inexpensive and flexible laboratory equipment like the Texas Instrument CBL to collect real data for mathematical analysis.
The organization of material on the Web matches its natural organization better than the traditional linear organization of material in a book. In fact, the organization of Multivariable Calculus, Linear Algebra, and Differential Equations in a Real and Complex World has been greatly influenced by Web-thinking as we put together this package.
So then, if the Web is so great -- why the book? The answer is, in part, we aren't sure. Books do have lots of advantages -- they are portable, don't require an AC outlet or a battery, and don't need a network connection. It is easier to read text on the printed page than on the screen and most of us don't curl up with a good computer the same way we curl up with a good book. For these reasons the book is more leisurely -- more wordy and chatty -- than this web-based material.
You will probably find your own best way to use the combination -- book and Web -- and your solution will depend on your tastes and circumstances -- for example, if your access to the Web is limited then you will probably use your book more than someone who has unlimited and convenient Web access.
Each module on the Web matches a section in Multivariable Calculus, Linear Algebra, and Differential Equations in a Real and Complex World. You will probably find your time on the Web more productive if you skim the corresponding section in the book beforehand and if you read that section afterward as a summary. In addition, the book will serve as a reference source when you are away from the computer, the network is down, or the power is off.