Essential Calculus Metric Version (Custom Solutions) (Paperback)
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The most important way to foster conceptual understanding is through the problems that we assign. To that end I have devised various types of problems. Some exercise sets begin with requests to explain the meanings of the basic concepts of the section.
Another type of exercise uses verbal description to test conceptual understanding. I particularly value problems that combine and compare graphical, numerical, and algebraic approaches.
●Graded Exercise Sets
Each exercise set is carefully graded, progressing from basic conceptual exercises and skill-development problems to more challenging problems involving applications and proofs.
My assistants and I spent a great deal of time looking in libraries, contacting companies and government agencies, and searching the Internet for interesting real-world data to introduce, motivate, and illustrate the concepts of calculus. As a result, many of the examples and exercises deal with functions defined by such numerical data or graphs.
One way of involving students and making them active learners is to have them work (perhaps in groups) on extended projects that give a feeling of substantial accomplishment when completed. I have included some projects: Applied Projects involve applications that are designed to appeal to the imagination of students. Discovery Projects anticipate results to be discussed later or encourage discovery through pattern recognition.
1. FUNCTIONS AND LIMITS.
3. APPLICATION OF DIFFERENTIATION.
5. APPLICATIONS OF INTEGRATION.
6. INVERSE FUNCTIONS: EXPONENTIAL, LOGARITHMIC, AND INVERSE TRIGONOMETRIC FUNCTIONS.
7. TECHNIQUES OF INTEGRATION.
8. FURTHER APPLICATIONS OF INTEGRATION.
9. PARAMETRIC EQUATIONS AND POLAR COORDINATES.
10. INFINITE SEQUENCES AND SERIES.
11. VECTORS, VECTOR FUNCTIONS AND THE GEOMETRY OF SPACE.
12. PARTIAL DERIVATIVES.
13. MULTIPLE INTEGRALS.