Inverse Problems : Activites for Undergraduates

Text in English. 222 pp. Couple pencil markings on one page. Inverse problems are hard to define. Yet nearly all mathematicians recognize an inverse problem when they see one. As children we learn about the direct problem of multiplication; given two numbers we find their product. The corresponding inverse problem is to find a pair of factors of a given number. This book introduces mathematics instructors to inverse problems and provides them with resources that are useful for teaching the lessons of inverse problems to students in the first two undergraduate years. The problems are introduced by an historical essay that provides, without any formal mathematics, a scientific and cultural context for the mathematical lessons that follow. The next four chapters deal with inverse problems in Precalculus, Calculus, Differential Equations and Linear Algebra. Each chapter contains six modules on specific inverse problems in the subject matter of the chapter. The modules consist of brief introductions for the teacher, an Activities section for students, and a concluding section of notes and suggestions for further reading Scripts in MATLAB keyed to Computations in the modules are provided in an appendix (the M-files may be downloaded from the author's Webpage). Each module opens with advice on the course level of the module, mathematical and scientific prerequisites, and the type of technology appropriate for the module.…