Book Review: Mathematics for Physicists

A book review on Mathematics for Physicists This new book by B. R. Martin and G. Shaw [1] is part of the Manchester Physics Series, a long-established set of elementary texbooks aimed primarily at providing undergraduate physics students (but also students in other physical sciences, such as astronomy, chemistry, earth and planetary science, etc.) with relatively short, self-contained courses on a number of subjects (including waves, electromagnetism, statistical physics, relativity, quantum mechanics, computer programming and nuclear physics) which are usually covered, at least at an introductory level, in the first 2 years of a typical modern physics degree. Specifically, the book aims to fill the gap between most contemporary high-school mathematics syllabuses and the mathematics needed for a typical undergraduate degree in physics. The book is well written and organized and it does a good job in the first two chapters of reviewing the basic elements of Euclidean geometry, trigonometry, real numbers, algebra, real variables, and elementary functions which are needed in the sequel. The authors rightly recognize that students often enter university with a variety of mathematical backgrounds. Moreover, they are clearly well aware of the fact that, in the experience of most instructors, even students with good mathematical prerequisites usually need experience using the mathematics to handle it efficiently and to develop useful intuition. The authors do achieve a good balance of formal development and pedagogic illustration by providing many worked out examples throughout the chapters, which both clarify and concretize the concepts or techniques introduced in the main body of the text and highlight useful applications in physics or engineering. In addition, a set of problems is given at the end of each chapter, which mostly provide concrete applications of the material covered in that chapter, but sometimes also introduce new concepts or topics which are left out of the main presentation to avoid digressions (examples include the first law of thermodynamics in problem 7.6, and Gaussian distributions in problem 13.22). Solutions to all the problems are provided in compact form at the end of the book. The treatment will be attractive and useful for lecturers looking for instructive and stimulating material to include, and it will be accessible to most students, including undergraduate students enrolled for an undergraduate university degree and those studying on their own. The equally competent treatment of the remaining material, which will be new to most students embarking on the course, is …