Review of Mathematics of Physics and Engineering

This text is designed for a course typically given in the junior or senior year, addressed to scientists (especially physicists and chemists) and engineers, detailing various topics in mathematics that arise in those disciplines. Generally these courses assume some knowledge of physics, and a mathematical background that consists of an introductory sequence through multivariate calculus, and first courses in linear algebra and differential equations. Major topics typically include vector analysis, complex analysis, Fourier analysis, and partial differential equations. The popular and/or classic texts that come to mind in this category include, for example, Arfken and Weber’s Mathematical Methods for Physicists, Boas’s Mathematical Methods in the Physical Sciences, or Kreyszig’s Advanced Engineering Mathematics. Although it plays a similar role, Blum and Lototsky takes an unconventional approach. The topics are more focussed and many are out of the scope of these other textbooks. In a nutshell, it puts much greater emphasis on the interplay between mathematics and physics, and goes to great lengths to involve the reader. This is discussed at some length in the last section of this review.