Calculus Mysteries and Thrillers

Even though they may be well-written, most mathematics books follow a set formula of presentation that is stale to many. While it may be an alien language to the uninitiated, the theorem - proof style has proven to be a very effective method of data transfer. However, not everyone understands these protocols, which is where books like this are worth their weight in ancient antiquities. Writing good problems that have a clear relevance to something that might actually happen is difficult, but not impossible, and this book is an existence proof of that. Eleven problems are given in the book, with the solution presented in the context of an official summary or report of how the conclusions were arrived at. In the first part of the book, there are short summaries of the problems with a list of what the precise mathematical requirements are for solution. This is an invaluable guide to anyone considering using the book as a classroom supplement. All problems require some topic commonly covered in a full year course of calculus. Topics such as the intermediate value theorem, the chain rule, Newton's method, the quotient rule, Newton's Law of Cooling and the Fundamental Theorem of Calculus are needed for solution. The first problem deals with the possibility of a fraud in connection with a parabolically shaped pool table and is presented as evidence to be used in a court of law. While the teaching of calculus has been invigorated somewhat recently with the introduction of sophisticated mathematical software, it still lacks some real-world applicability. If you are searching for problems to present to a class that will really be of interest, you will find none better than the eleven in this book. Published in Journal of Recreational Mathematics, reprinted with permission.