The authors of this volume have assembled a collection of projects students
will find lively and stimulating. They can be used by the average calculus
student, and are solvable with guidance and instruction from the teacher.
Some of the projects cover a variety of calculus topics for the first year of
a typical single-variable calculus program, while others are applicable to
multivariable calculus. The subject matter is as diverse as the prerequisites.
Some of the material involves concepts you would expect to find in any calculus
course, while other material will lead the student to examine an interesting
application or theory that is tangential to the core material. Several projects
involve maxima and minima applications, others grapple with concepts such as
surfaces and Riemann sums, and still others encourage expansions on the work of
Newton and Archimedes.
Students will learn how to use calculus to solve real problems. How to use
the library to ding mathematical sources, how to read and write mathematical
material, and how to cooperate with their peers in the solution of a difficult
problem. Learning that they can solve what at first seems an inscrutable
mathematical problem can only increase their mathematical confidence.
Each project is self-contained, including a brief statement of the problem
for the students and more thorough information for the teacher. The detailed
information provided by the authors will lessen the amount of time such a
project might require of the teacher.