This volume of problems has been produced under the auspices of a calculus reform project funded by the National Science Foundation. Its aim is to address the need, expressed by many mathematicians, for a fresh approach to the study of elementary calculus at the college level. In particular, we seek to provide a collection of textbook problems which stimulates students to understand the power and the beauty of calculus rather than to regard the subject as a hodgepodge of unrelated techniques.
The current calculus reform movement has developed a number of themes and ideas which this collection attempts to incorporate. It is now apparent that the existence of computer algebra systems (CAS) transforms the study of calculus by providing students with a powerful resource for computations, graphical representation, and symbolic manipulation. In this environment, many of the problems calculus students traditionally see become trivialities, and we have, therefore, avoided such problems. Our exercises stress conceptual understanding over rote drill. Ocassionally this is done by asking students to use the computer’s output to make a conjecture. Sometimes we ask students to formulate the answer toa problem and to leave the calculation to a computer package or a calculator.
In this way, interesting problems that were once thought too hard for students because of their computational difficulties are now accessible. More often, however, our exercises neither require the use of a CAS nor are they trivialized by one. An effort has been made to convey functions by graphs and tables, rather than by rules in the belief that “real world” data generally come that way.