Differential and Integral Calculus Through Problems and Solutions

For a number of reasons, the current basic calculus course is a mere shadow of what it was in previous generations. One of the main symptoms of this decline has been the essential automation of these courses where students no longer have to do any real thinking. This is because the course is built around exact answer problems in closed form, where calculators and computers can easily spit out answers. While a lot of mathematicians decry the loss of rigorous proofs in such courses, such as calculating limits precisely with inequalities, that's really just the most obvious loss. A more subtle loss has been the downplaying of the roles of algebra and elementary geometry that were so essential to pre-university training and played such critical roles not only in those calculus courses, but physics and engineering as well. Being able to analyze, set up and grind out lengthy computations forced students to not only understand calculus, but master the underlying preliminary skills they learned earlier far better. The republication of this wonderful collection by Petersen and Grasser, among other things, looks to expose today's students to the solutions of these kinds of problems to improve these skills. It also provides an excellent snapshot in a reasonably short volume of what the kinds of calculus courses we mourn the loss of consisted of and that the OSC Series is looking to resurrect. Petersen and Grasser isn't really a complete study guide to calculus, it's not complete enough for that. It doesn't have exercises for a student to work out nor detailed discussions of the topics each problem represents. What P&G does is provide a rapid overview of the subject through detailed solutions of problems representative of all the major topics that were typically covered in such a course when it was published. Richly diverse in its choice of problems with step by step detailed solutions and many visual illustrations, this inexpensive collection will become a treasured study supplement for both students and teachers of calculus at various levels, from introductory to advanced level.