Studies in Theoretical Physics : Fundamental Mathematical Methods

Studies in Theoretical Physics, Volume 1: Fundamental mathematical methods is the first of the six-volume series in theoretical physics. It provides the mathematical methods that any physical sciences and engineering undergraduate might need in upper-division courses in classical mechanics, quantum mechanics, and electricity and magnetism. It is a book designed for a two-semester course in Mathematical Methods. The first eight chapters introduce series and sequences, complex numbers, functions and series, vectors, matrices and determinants, and differential and integral calculus of scalar and vector functions, suitable for the first semester of a two-semester sequence. The last eight chapters introduce the calculus of variations, linear algebra, power series substitution method for solving differential equations, partial differential equations, contour integrals, Laplace transforms, Fourier series, and Fourier transforms, suitable for the second semester. Unlike other books, this book has a section at the end of each chapter that focuses on solving problems using Mathematica.

Key Features

• All selected topics provide the mathematical methods students would need in Classical Mechanics, Electricity and Magnetism, and Quantum Mechanics at the undergraduate level.
• Modern 3D graphics are extensively used for 3D visualization and a better understanding of the topics covered and the example problems used.
• Examples are selected to cover the applications in the subsequent volumes of Studies in Theoretical Physics.
• Topics covered in sixteen chapters are intended for a two-semester sequence of undergraduate courses in Mathematical Methods. Each chapter also introduces Mathematica to the topics covered by re-solving most of the example problems considered in each chapter.
• Discussions are clear, brief, concise, and use simple English easy to understand by readers with English as a second language.
• The authors of this book have years of experience teaching many introductory and upper-division physics courses.

Dr. Daniel Erenso has been working as a professor of physics at Middle Tennessee State University (MTSU) since 2003. He received his PhD (2003) from the University of Arkansas (UA), Advanced Diploma (1999) from Abdul Salam International Center for Theoretical Physics (ASICTP), a BSc (1990), and MSc (1997) from Addis Ababa University (AAU) in physics. For decades, Dr. Erenso has taught, researched, and mentored at different universities. He has taught several introductory and advanced physics courses. He received the MTSU College of Basic & Applied Sciences (CBAS) Excellence in Teaching Award in 2011. Inspired by the COVID19 pandemic, he has recently published a book, Virtual and Real Labs for Introductory Physics II Optics, modern physics, and electromagnetism. Dr. Erenso has also maintained active theoretical and experimental physics research in quantum optics and biomedical optics. He has published more than 36 and presented over 60 research works. He has received Sigma Xi the Scientific Research Society Aubrey E Harvey, outstanding graduate research award from the UA (2003), MTSU Foundations Special Project Award (2005), MTSU, CBAS Distinguished Research Award (2016), and a nomination for American Physical Society (APS) Prize for a Faculty Member for Research in an Undergraduate Institution (2020). His excellence in teaching and research earned him the Fulbright Scholar Award in 2016.

Dr. Victor Montemayor teaches Physics and Advanced Mathematics at Germantown Academy (GA) in Fort Washington, PA. He retired from Middle Tennessee State University (MTSU) in 2015 after serving for 25 years as Professor of Physics. Dr. Montemayor has received numerous awards for Teaching, Learning, and Innovative Educational Technology from both MTSU and GA. He was also the recipient of the 2013 Ernest L. Boyer International Award for Excellence in Teaching, Learning, and Technology. Dr. Montemayor received BS degrees in Physics and Mathematics from Bucknell University and the PhD degree in Theoretical Physics from the University of Toledo. He was a visiting scientist at the Hahn-Meitner Institute for Nuclear Research in Berlin, Germany and at the Institute for Atomic Research of the Hungarian Academy of Sciences in Debrecen, Hungary prior to accepting the position at MTSU. Dr. Montemayor has enjoyed teaching many different courses in physics, from introductory to advanced undergraduate-level courses. He was chair of the Committee on Medical Physicists as Educators and a member of the Education Council of the American Association of Physicists in Medicine for 11 years. Dr. Montemayor is currently completing another book introducing undergraduate science majors to the field of Medical Physics.