An Introduction to Capstone in Applied Analysis

Inverse problems are one of the oldest, most important mathematical problems in science and engineering. However, the field of inverse problems has undergone rapid development in the last two decades due to the massive increase in computing power and the development of powerful numerical techniques such as finite difference method, finite element method, finite volume method and spectral method. Because of their applications in medical imaging, underground prospecting, nondestructive testing, astronomical imaging, image processing, remote sensing, and data mining, the Business, Industry and Government (BIG) sectors are very interested in applied inverse problems. Despite its great importance and demand, there is no project oriented applied and computational inverse problem book that can be adapted as a text for senior undergraduates as their capstone experience and pathway to research in applied analysis. The goal of this book is to fill this gap and provide opportunity to students, professors and researchers in biosciences, applied sciences, applied-computational mathematics, engineering, mathematical programming, mathematical economics, mathematical biology and optimization via applied and computational inverse problem projects. This book is sequenced as three major parts. The part of the book that includes chapters 1, 2 and 3 highlights major concepts including results in applied analysis. The second part of the book that includes chapters 4 and 5 displays the key numerical methods and programming in MATLAB. The final part of the book that includes chapters 6, 7, 8, 9, 10, 11 and 12 showcases several inverse-problem-related projects done with students.