Calculus: Concepts and Connections is a readable introduction to the basic topics of single and multivariable calculus from the basic idea of limits up through Stokes' Theorem. It is a textbook clearly aimed at the "average" student. The main difference between this and other comparable textbooks such as Stewart's Calculus is that explanations of concepts and examples are more extensive and more explicit attempts are made to establish the connections between concepts. The standard topics are treated in more or less the usual order.
The authors have obviously taken pains to develop good exercise sets. Typically, each chapter has writing exercises, a collection of fairly routine problems, exercises designed to use a graphing calculator or computer algebra system, and exploratory problems. The latter are intended to be more challenging and to provoke a deeper level of understanding. A nice feature in the text is the use of an icon to identify pitfalls arising from injudicious use of calculators or computer algebra systems.
There are well over two hundred explicit examples of applications in the text or in exercises; these fall into the general categories of biology, chemistry, economics, physiology, engineering, physics and sports. While these are not especially deep applications, they generally have enough meat on them to be interesting.
Intuitive explanations and arguments of plausibility are usually favored over proofs, though there are a variety of proofs of varying levels of generality and rigor. In addition, there is an appendix with more rigorous proofs of some results.
This would be an appealing self-study text as well as a good choice for a class of average ability. It would probably seem too slow moving for strong students.
Bill Satzer (email@example.com) is a senior intellectual property scientist at 3M Company, having previously been a lab manager at 3M for composites and electromagnetic materials. His training is in dynamical systems and particularly celestial mechanics; his current interests are broadly in applied mathematics and the teaching of mathematics.