Title
Applied Analysis (Dover Books on Mathematics),New
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This is a basic text for graduate and advanced undergraduate study in those areas of mathematical analysis that are of primary concern to the engineer and the physicist, most particularly analysis and design of finite processes that approximate the solution of an analytical problem. The work comprises seven chapters:Chapter I (Algebraic Equations) deals with the search for roots of algebraic equations encountered in vibration and flutter problems and in those of static and dynamic stability. Useful computing techniques are discussed, in particular the Bernoulli method and its ramifications.Chapter II (Matrices and Eigenvalue Problems) is devoted to a systematic development of the properties of matrices, especially in the context of industrial research.Chapter III (LargeScale Linear Systems) discusses the 'spectroscopic method' of finding the real eigenvalues of large matrices and the corresponding method of solving largescale linear equations as well as an additional treatment of a perturbation problem and other topics.Chapter IV (Harmonic Analysis) deals primarily with the interpolation aspects of the Fourier series and its flexibility in representing empirically given equidistant data.Chapter V (Data Analysis) deals with the problem of reduction of data and of obtaining the first and even second derivatives of an empirically given function constantly encountered in tracking problems in curvefitting problems. Two methods of smoothing are discussed: smoothing in the small and smoothing in the large.Chapter VI (Quadrature Methods) surveys a variety of quadrature methods with particular emphasis on Gaussian quadrature and its use in solving boundary value problems and eignenvalue problems associated with ordinary differential equations.Chapter VII (Power Expansions) discusses the theory of orthogonal function systems, in particular the 'Chebyshev polynomials.'This unique work, perennially in demand, belongs in the library of every engineer, physicist, or scientist interested in the application of mathematical analysis to engineering, physical, and other practical problems.
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- Q: What topics are covered in 'Applied Analysis'? A: 'Applied Analysis' covers a range of topics including Algebraic Equations, Matrices and Eigenvalue Problems, Large-Scale Linear Systems, Harmonic Analysis, Data Analysis, Quadrature Methods, and Power Expansions.
- Q: Who is the author of this book? A: The book is authored by Cornelius Lanczos, a noted mathematician and physicist.
- Q: Is this book suitable for beginners? A: This book is primarily intended for graduate and advanced undergraduate students, so some prior knowledge in mathematical analysis is recommended.
- Q: What is the publication date of 'Applied Analysis'? A: 'Applied Analysis' was published on July 21, 2010.
- Q: How many pages does this book have? A: The book contains a total of 576 pages.
- Q: What is the binding type of this book? A: This edition of 'Applied Analysis' is available in paperback binding.
- Q: What is the main focus of Chapter I? A: Chapter I focuses on Algebraic Equations, specifically addressing the search for roots of equations encountered in vibration and flutter problems.
- Q: Does this book include any practical applications? A: Yes, the book discusses practical applications of mathematical analysis in engineering and physical problems throughout its chapters.
- Q: Are there any methods for data analysis discussed? A: Yes, Chapter V specifically addresses data analysis techniques, including methods for curve fitting and obtaining derivatives of functions.
- Q: Can this book help with understanding eigenvalue problems? A: Yes, the book includes a dedicated chapter on Matrices and Eigenvalue Problems, which systematically develops their properties and applications.