Users Product Reviews: |
Product Review Summary: You could do a whole lot worse. This is a beautifully written book! This is a great place to start and perhaps end one's study of boundary and eigenvalue problems. The first chapter even provides one of the best treatments of first variation I have seen in print. The vibrating string, heat conduction, PDEs, Fourier series,special functions, self-adjoint operators, it is all there and written in an easy to understand format. Some may find the notation a little dated but that is little price to pay for such a treasure of knowledge. Read and enjoy.
Product Review Summary: A treatise for starting a career I bought Sagan's book while a senior, and used it for a text while a second year professional and a third year graduate student in mathematics. The course led to a series of courses in theoretical mechanics, and untimately, a doctorate in control theory. The course taught from this book, and the following course in mechanics provided a strong foundation for a career. I continue to have my students read Sagan's book.
Product Review Summary: Physical problems treated with mathematical rigor. This text includes material usually covered in mathematical physics courses, but its approach is somewhat different, and better, than most of the classics. The point is that the author felt not content with just explaining how to employ the most common mathematical methods to solve physical problems. He, on one hand, presents full motivation from the physical point of view, while on the other hand keeping high-level mathematical rigor. Believe me: this is not usual in mathematical physics books. By doing so, the author has produced a text valuable for both physicists and mathematicians.Its contents are: Hamilton's principle and the theory of the first variation, representation of some physical phenomena by partial differential equations, theorems related to partial differential equations and their solutions, fourier series, self-adjoint boundary value problems, Legendre polynomials and Bessel functions, characterization of eigenvalues by a variational principle, spherical harmonics, the nonhomogeneous boundary value problem. Includes excercises for most sections and references for each chapter. Suitable for third year undergraduates and on.
Product Review Summary: A high-class, beautifully written text The problem with books on mathematical methods for physics is that they look more like a collection of recipes than like a coherent text. This was not true of the older classics, like Sommerfeld's "Partial Differential Equations of Physics". Fortunately, there is this beautiful book by Hans Sagan, now on Dover catalogue, to follow that tradition. A highlight is his treatment of the Sturm-Liouville problem. Having previously introduced variational methods, he shows that there is a "Lagrangian" whose "Euler-Lagrange equations" are just the Sturm-Liouville equations. In so doing, he has all the arsenal of approximation methods of variational calculus at his disposal to apply in the so-called special functions. As a beautiful example he estimates the position of the zeros of Bessel functions. The reader will find many other mathematical gems in this fine text.
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