An Introduction to Capstone in Applied Analysis: A Fundamental Guide for Students and Instructors


Narayan Thapa
Cameron University, Department of Mathematical Sciences, Lawton, OK, USA

Series: Mathematics Research Developments
BISAC: MAT003000
DOI: 10.52305/HXVO8994

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.
(Imprint: Nova)


Table of Contents

Table of Contents


Chapter 1. Vector Spaces

Chapter 2. Normed Linear Spaces

Chapter 3. Hilbert Spaces

Chapter 4. Numerical Methods

Chapter 5. Programming with MATLAB

Chapter 6. Inverse Problem in Finance

Chapter 7. Inverse Problem in Physics 1

Chapter 8. Inverse Problem in Physics 2

Chapter 9. Inverse Problem in Medicine 1

Chapter 10. Inverse Problem in Physics 3

Chapter 11. Inverse Problem in PDE

Chapter 12. Inverse Problem in Medicine 2



“This is an excellent reference for anyone interested in applied analysis, especially for students and teachers working on Science, Technology, Engineering and Mathematics (STEM) capstone projects. It is an easy to read textbook that will help build mathematical foundations needed for capstone projects with plethora of examples in wide range of applications.” – Sudhir Shrestha, Ph.D., Department of Engineering Science, Sonoma State University, Rohnert Park, California

“A surge in undergraduate and capstone research has been noticed in the past several years. This is due to the great explosion in the advancement of technology. The traditional class courses taken are not enough anymore. This book aims to facilitate students and instructors working in capstone and undergraduate research projects. The book is written well, carefully designed for undergraduate students in mathematics and applied sciences. We see that we are looking at a very analytic and easy to read map in the exciting area of capstone projects, written by an experienced mathematician. It is certainly a must-read book. We strongly and enthusiastically recommend it for usage in classroom or as a study guide for capstone projects. – Ioannis K. Argyros, Ph.D., Professor, Department of Mathematical Sciences, Cameron University, Lawton, Oklahoma

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