The mathematical mechanic Using physical reasoning to solve problems

The Mathematical Mechanic is a pleasant surprise. From the book's description, this reviewer expected a series of application problems that might have been of some use in academic coursework. Instead he found a very engaging set of exercises that he will definitely use in classes and will do on his own for some time to come. Levi (math, Penn State) gives physical examples (e.g., "Saving a Drowning Victim by Fermat's Principle," "The Cheapest Can," "How Much Gold Is in a Wedding Ring?") that demonstrate a large array of mathematical proofs. Though, as he indicates, his physical examples do not constitute rigorous proofs, they do give insight and allow for intuition to guide readers to mathematical relations. For example, he finds the center of mass of an object by calculating the work done by two different methods--avoiding the messy integrals. He examines a wide range of physics and addresses most topics covered in an undergraduate's first year. Though much of the mathematics does not go beyond precalculus, students who have finished a year of calculus would benefit the most from the book. The appendixes provide quick reviews of the physics used. Valuable to engineers, physicists, and mathematicians at all levels. Summing Up: Highly recommended. Lower-division undergraduates through professionals/practitioners. E. Kincanon Gonzaga University