Studies in Theoretical Physics, Volume 1

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.

Author Biography

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.