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Fourier Series and Orthogonal Functions (Dover Books on Mathematics), by Harry F. Davis
Download Fourier Series and Orthogonal Functions (Dover Books on Mathematics), by Harry F. Davis
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This incisive text deftly combines both theory and practical example to introduce and explore Fourier series and orthogonal functions and applications of the Fourier method to the solution of boundary-value problems. Directed to advanced undergraduate and graduate students in mathematics as well as in physics and engineering, the book requires no prior knowledge of partial differential equations or advanced vector analysis. Students familiar with partial derivatives, multiple integrals, vectors, and elementary differential equations will find the text both accessible and challenging.
The first three chapters of the book address linear spaces, orthogonal functions, and the Fourier series. Chapter 4 introduces Legendre polynomials and Bessel functions, and Chapter 5 takes up heat and temperature. The concluding Chapter 6 explores waves and vibrations and harmonic analysis. Several topics not usually found in undergraduate texts are included, among them summability theory, generalized functions, and spherical harmonics.
Throughout the text are 570 exercises devised to encourage students to review what has been read and to apply the theory to specific problems. Those preparing for further study in functional analysis, abstract harmonic analysis, and quantum mechanics will find this book especially valuable for the rigorous preparation it provides. Professional engineers, physicists, and mathematicians seeking to extend their mathematical horizons will find it an invaluable reference as well.
- Sales Rank: #514825 in eBooks
- Published on: 2012-09-05
- Released on: 2012-09-05
- Format: Kindle eBook
Most helpful customer reviews
28 of 31 people found the following review helpful.
FOURIER SERIES, THE SOLUTION TO ALL ENGRG PROBLEMS.
By WINSTON OLADAPO
During the course of my studying the book, i discovered that the book goes indepth in making the concept of fourier series analysis simplified. As an engineer i make use of fourier series applications often both in my research work and in the teaching of my students to a great extent i have found this book extremely useful in that it aids the level of understanding. I have also realised that even to a novice that picks up this book will find it very interesting to a large extent.As it is known that fourier series is very usefu in engineering study , especially in the area of solving heat condition problems and for specific applications in engineering design. The book has taken a more comprehensive form which makes reading very easy . I prefer this book because it follows a progressive sequence of explanation.The introduction of fourier integral into the fourier series solution has brought to a great extent the use of partial differential equations in eral life engineering problems . The book has also made the engineering concepts defined practicable, by demonstration of a straight forward attempt aimed at pionting out the extent to which engineerig is usefuk in our everyday lives. This book should be recomended in schools as the true book avalaible in the understanding of the concept of fourier series. Orthogonal function study has also been made in such a way that a first time reader will find it easy in terms of the concept and context.
19 of 20 people found the following review helpful.
Rigor and intuition -- a classic
By Ken Braithwaite
I learned Fourier analysis on my own, and mostly from this book. Its intuitive content is excellent, but it is a rigorous math text, approaching the subject form an algrbraic viewpoint. He treats convergence issies in detail and in a well-motivated fashion. "Read Who is Fourier" for an intro, and read this for the math behind the intuition.
9 of 9 people found the following review helpful.
EXCELLENT
By student
This is one of the best mathematics books I've been fortunate enough to come across as someone with a B.S in mathematics and as a current graduate student. The explanations are very clear, and details typically left out by other authors are included, whether it be in definitions, concepts, proofs, or examples. The title is somewhat deceiving in that much more material is covered than one would think. If I could give this book 6 stars, I certainly would.
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