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Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics) ReviewWhen I took undergraduate quantum mechanics 30 years ago, we learned a lot about Louis deBroglie, Max Planck, the photoelectric effect, then moved into wave functions, the Schroedinger equation, simple one-dimensional potentials and the hydrogen atom. Maybe there was a little angular momentum tossed in. It was not until graduate school that I learned much about/X> = xi/x>
where /X> is a vector in an n-dimensional, linearly independent vector space and the xi's were its components in the basis /x>. A lot of things like representations might have made more sense. Anyway, Hassani's undergraduate text gives one an excellent view of vectors and coordinate systems. In particular, it trains one well to leap into the more abstract view of vectors one reads about in, say, R. Shankar's excellent book on quantum mechanics, and also gives one a good deal of exercise on how to translate between coordinate systems. In graduate school, I found the ability to roam between coordinate systems to be very, very handy and the laborious time spent learning it was worth it. I'm not done with this book yet. I'm now getting into his chapters on complex variables and differential equations, but Hassani's treatment of vectors and coordinate systems is very good indeed. Undergraduate physics students who plan to go on into graduate school will find time with this book well spent.Mathematical Methods: For Students of Physics and Related Fields (Lecture Notes in Physics) OverviewIntended to follow the usual introductory physics courses, this book has the unique feature of addressing the mathematical needs of sophomores and juniors in physics, engineering and other related fields. Many original, lucid, and relevant examples from the physical sciences, problems at the ends of chapters, and boxes to emphasize important concepts help guide the student through the material.Beginning with reviews of vector algebra and differential and integral calculus, the book continues with infinite series, vector analysis, complex algebra and analysis, ordinary and partial differential equations. Discussions of numerical analysis, nonlinear dynamics and chaos, and the Dirac delta function provide an introduction to modern topics in mathematical physics.This new edition has been made more user-friendly through organization into convenient, shorter chapters. Also, it includes an entirely new section on Probability and plenty of new material on tensors and integral transforms.
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