Scalars and Vectors. Tensors. Partial Differential Equations and Modelling. Symmetries and Group Theory. Function Spaces. Eigenfunction Expansions. Green’s Functions. Variational Calculus. Calculus on Manifolds. Classical Mechanics and Field Theory. Reference material. Summaries of Chapters.
Mattias Blennow is an associate professor in the Department of Theoretical physics at KTH Royal Institute of Technology, Stockholm, Sweden. His field of research is directed towards weakly interacting particle physics, specializing in theoretical neutrino and dark matter physics with 51 scientific papers published in peer-reviewed journals. He has taught courses at all university levels, including mathematical methods in physics, quantum mechanics, special and general relativity, and quantum field theory.
Many of my favorite reference texts manage to resolve a paradox :
how to provide an original presentation of well-established
material? For example, both "The Feynman Lectures" (Richard
Feynman) and "Introduction to Error Analysis" (John Taylor) are
justifiably well-known because of their idiosyncratic approach to
the subject at hand. There are other, similarly engaging texts, and
I’m pleased to describe a new addition to my list, "Mathematical
Methods for Physics and Engineering" by Mattias Blennow. Prof.
Below has written a text that will compete in a crowded field;
‘standard texts’ such as those by Boas, Shankar, and Arfken are
well-known and widely adopted. However, Blennow’s text offers much
that substantially improves upon these others and deserves serious
consideration for textbook adoption. The intended audience is
likely an advanced undergraduate or introductory graduate course in
Physics or Engineering departments, and the worked examples and
end-of-chapter problems bear this out. The overall focus of this
book is to apply mathematical tools (for example, eigenfunction
expansions) to solve physics and engineering problems.Personally,
several chapters stand out: Chapter 4 (Group theory) is the
friendly introduction that I have long sought. Example problems are
particularly well-chosen and insightful. Similarly, Chapter 7
(Green’s Functions) contains material that does not appear to be
available outside of specialized mathematics texts. Another
highlight includes a particularly clear discussion about
Sturm-Liouville problems in Chapter 5.The end-of-chapter problems
are well considered and span a wide range of difficulty, making
them suitable for homework problems. I strongly recommend that
anyone teaching an advanced undergraduate or early graduate class
on "Mathematical Methods for Physics" peruse this book and consider
using it.-Andrew Resnick, Associate Professor, Department of
Physics, Cleveland State UniversityMost math textbooks focus on
math itself (e.g. proving a theorem strictly) and do not connect
math with physics, making them not very useful for physicists,
chemists, or engineers. Books that emphasize the "application"
aspect of math will be of great value to these readers but are
unfortunately rare to find, especially in the form of textbook
instead of general reference/manual. This book does a nice job
towards filling the gap. I envision that students who major in
physics and engineering, especially those who are interested in
gaining good understanding of the theoretical aspects of physics,
will like this book.- Prof. Dr Hai Lin, University of Colorado
DenverI wish I had this book available as an advanced undergraduate
and graduate student of physics. The challenge for both a student
and a teacher of physics is that usually the mathematics one needs
in the physics or engineering standard course lectures is not yet
avaialable. Here one finds the material presented in a very
intuitive way, with an emphasis on how the concepts are applied to
calculations in physics. The concepts themselves are introced using
typical examples for their use in physics. This does not only
include the usual vector and calculus, partial differential
equations, and special functions, but also a very valuable
introduction to group and group-representation theory, whose
importance for physics cannot be overestimated. The book also
covers functional analysis, variational calculus, and differential
geometry on manifolds. This provides a rather complete mathematical
basis for all the standard subjects of the physics and engineering
curriculum from classical point and continuum mechanics and
electrodynamics to quantum mechanics and general relativity. and
thus it is not only a textbook for students and teachers but also a
valuable reference work for any user of mathematical methods in the
natural and engineering sciences.
- Hendrik van Hees PD, Insitute for Theoretical Physics, Goethe
University Frankfurt am Main.This book is a comprehensive
introduction to mathematical methods most widely used by physicists
and engineers. It is written with a great pedagogic skill and
contains a large number of carefully selected and thoroughly
worked-out examples, which serve as a perfect illustration of the
presented material and facilitate its mastering. The many problems
given at the end of each chapter will help the reader to further
improve his or her practical command of the material. Compared to
other similar books, it is more accessible to undergraduate-level
students as it does not rely on examples based on advanced topics,
such as quantum mechanics. The book can serve as a textbook as well
as a handy reference book. Highly recommended.- Evgeny Akhmedov,
Staff member at the Max Planck Institute for Nuclear Physics,
Heidelberg and Senior Research Scientist at the Kurchatov Institute
of Atomic Energy, Moscow
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