Laboratory Projects involve technology; the one following Section Suggested references are supplied. Discovery Projects anticipate results to be discussed later or encourage discovery through pattern recognition see the one following Section 7. Others explore aspects of geometry: tetrahedra after Section Problem Solving Students usually have difficulties with problems for which there is no single well-defined procedure for obtaining the answer. They are applied, both explicitly and implicitly, throughout the book.
After the other chapters I have placed sections called Problems Plus, which feature examples of how to tackle challenging calculus problems. Here I reward a student significantly for ideas toward a solution and for recognizing which problem-solving principles are relevant.
Dual Treatment of Exponential and Logarithmic Functions There are two possible ways of treating the exponential and logarithmic functions and each method has its passionate advocates. Because one often finds advocates of both approaches teaching the same course, I include full treatments of both methods. In Sections 6. Students have seen these functions introduced this way since high school. In the alternative approach, presented in Sections 6. This latter method is, of course, less intuitive but more elegant.
You can use whichever treatment you prefer. If the first approach is taken, then much of Chapter 6 can be covered before Chapters 4 and 5, if desired. To accommodate this choice of presentation there are specially identified problems involving integrals of exponential and logarithmic functions at the end of the appropriate sections of Chapters 4 and 5.
This order of presentation allows a faster-paced course to teach the transcendental functions and the definite integral in the first semester of the course. For instructors who would like to go even further in this direction I have prepared an alternate edition of this book, called Calculus: Early Transcendentals, Eighth Edition, in which the exponential and logarithmic functions are introduced in the first chapter. May not be copied, scanned, or duplicated, in whole or in part.
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