Fourier Series and Orthogonal Polynomials by Dunham Jackson (PDF)

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User’s Reviews

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐A dream book for a pure mathematician and theoretical physicist. This was ordered for someone else but they were very happy with the content and price point!

⭐I was hoping for a more introductory treatment of the topic of Fourier Series. I am a math instructor trying to get a handle on the topic, and while I can follow the text, it is not one I would recommend to others seeking a high-level explanation and introduction. However, I am still looking and have not yet found a text that doesn’t immediately dive into a much more technical explanation than I wish.

⭐The preface of Dunham Jackson’s beautiful little book on Fourier Series and Orthogonal Polynomials is based on a course he refined over a period of years and this shows in the clear eyed exposition of the ideas. Early texts in mathematics and probability, such as Abraham de Moivre’s The Doctrine of Chances Or, a Method of Calculating the Probability of Events in Play, rely on verbal descriptions to the point of obscuring the equations, and many modern texts rely on equations to the point of obscuring the conceptual frame of needed to understand the equations. In contrast Dunham steers to the middle path between these extremes that presents both the ideas and the technical formulation alike and in parallel.The book covers important theorems for Fourier Series such as Riemann’s Theorem, Parseval’s Theorem, special hypotheses for uniform convergence, convergence at points of discontinuity, the least square property, Fejer’s Theorem on summability of Fourier Series of continuous functions, Weierstrass’s Theorem, and more. Yet this is presented in a way most accessible to engineers and mathematicians specializing in other fields.He moves on to other topics in orthogonal functions including:Legendre PolynomialsBessel FunctionsBoundary Value ProblemsWeight functionsJacobi, Hermite, and Laguerre PolynomialsConvergence properties.To summarize: If you want a clear exposition of the properties of key orthogonal systems then get this book.

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