A First Course on Orthogonal Polynomials

A First Course on Orthogonal Polynomials
Author: Kenier Castillo
Publisher: CRC Press
Total Pages: 226
Release: 2024-11-19
Genre: Mathematics
ISBN: 104015560X

A First Course on Orthogonal Polynomials: Classical Orthogonal Polynomials and Related Topics provides an introduction to orthogonal polynomials and special functions aimed at graduate students studying these topics for the first time. A large part of its content is essentially inspired by the works of Pascal Maroni on the so-called algebraic theory of orthogonal polynomials, which distinguishes it from other contributions in the field. Features Suitable for a graduate course in orthogonal polynomials Can be used for a short course on the algebraic theory of orthogonal polynomials and its applicability to the study of the “old” classical orthogonal polynomials Includes numerous exercises for each topic Real and complex analysis are the only prerequisites

An Introduction to Orthogonal Polynomials

An Introduction to Orthogonal Polynomials
Author: Theodore S Chihara
Publisher: Courier Corporation
Total Pages: 276
Release: 2011-02-17
Genre: Mathematics
ISBN: 0486479293

"This concise introduction covers general elementary theory related to orthogonal polynomials and assumes only a first undergraduate course in real analysis. Topics include the representation theorem and distribution functions, continued fractions and chain sequences, the recurrence formula and properties of orthogonal polynomials, special functions, and some specific systems of orthogonal polynomials. 1978 edition"--

Orthogonal Polynomials

Orthogonal Polynomials
Author: Gabor Szegš
Publisher: American Mathematical Soc.
Total Pages: 448
Release: 1939-12-31
Genre: Mathematics
ISBN: 0821810235

The general theory of orthogonal polynomials was developed in the late 19th century from a study of continued fractions by P. L. Chebyshev, even though special cases were introduced earlier by Legendre, Hermite, Jacobi, Laguerre, and Chebyshev himself. It was further developed by A. A. Markov, T. J. Stieltjes, and many other mathematicians. The book by Szego, originally published in 1939, is the first monograph devoted to the theory of orthogonal polynomials and its applications in many areas, including analysis, differential equations, probability and mathematical physics. Even after all the years that have passed since the book first appeared, and with many other books on the subject published since then, this classic monograph by Szego remains an indispensable resource both as a textbook and as a reference book. It can be recommended to anyone who wants to be acquainted with this central topic of mathematical analysis.

Frontiers In Orthogonal Polynomials And Q-series

Frontiers In Orthogonal Polynomials And Q-series
Author: M Zuhair Nashed
Publisher: World Scientific
Total Pages: 577
Release: 2018-01-12
Genre: Mathematics
ISBN: 981322889X

This volume aims to highlight trends and important directions of research in orthogonal polynomials, q-series, and related topics in number theory, combinatorics, approximation theory, mathematical physics, and computational and applied harmonic analysis. This collection is based on the invited lectures by well-known contributors from the International Conference on Orthogonal Polynomials and q-Series, that was held at the University of Central Florida in Orlando, on May 10-12, 2015. The conference was dedicated to Professor Mourad Ismail on his 70th birthday.The editors strived for a volume that would inspire young researchers and provide a wealth of information in an engaging format. Theoretical, combinatorial and computational/algorithmic aspects are considered, and each chapter contains many references on its topic, when appropriate.

A First Course in Numerical Methods

A First Course in Numerical Methods
Author: Uri M. Ascher
Publisher: SIAM
Total Pages: 574
Release: 2011-07-14
Genre: Mathematics
ISBN: 0898719984

Offers students a practical knowledge of modern techniques in scientific computing.

A First Course in the Numerical Analysis of Differential Equations

A First Course in the Numerical Analysis of Differential Equations
Author: A. Iserles
Publisher: Cambridge University Press
Total Pages: 481
Release: 2009
Genre: Mathematics
ISBN: 0521734908

lead the reader to a theoretical understanding of the subject without neglecting its practical aspects. The outcome is a textbook that is mathematically honest and rigorous and provides its target audience with a wide range of skills in both ordinary and partial differential equations." --Book Jacket.

A First Course in the Design of Experiments

A First Course in the Design of Experiments
Author: John H. Skillings
Publisher: Routledge
Total Pages: 696
Release: 2018-05-08
Genre: Mathematics
ISBN: 1351469975

Most texts on experimental design fall into one of two distinct categories. There are theoretical works with few applications and minimal discussion on design, and there are methods books with limited or no discussion of the underlying theory. Furthermore, most of these tend to either treat the analysis of each design separately with little attempt to unify procedures, or they will integrate the analysis for the designs into one general technique. A First Course in the Design of Experiments: A Linear Models Approach stands apart. It presents theory and methods, emphasizes both the design selection for an experiment and the analysis of data, and integrates the analysis for the various designs with the general theory for linear models. The authors begin with a general introduction then lead students through the theoretical results, the various design models, and the analytical concepts that will enable them to analyze virtually any design. Rife with examples and exercises, the text also encourages using computers to analyze data. The authors use the SAS software package throughout the book, but also demonstrate how any regression program can be used for analysis. With its balanced presentation of theory, methods, and applications and its highly readable style, A First Course in the Design of Experiments proves ideal as a text for a beginning graduate or upper-level undergraduate course in the design and analysis of experiments.

Fourier Series and Orthogonal Polynomials

Fourier Series and Orthogonal Polynomials
Author: Dunham 1888-1946 Jackson
Publisher: Hassell Street Press
Total Pages: 256
Release: 2021-09-09
Genre:
ISBN: 9781014791238

This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

A First Course in Random Matrix Theory

A First Course in Random Matrix Theory
Author: Marc Potters
Publisher: Cambridge University Press
Total Pages: 371
Release: 2020-12-03
Genre: Computers
ISBN: 1108488080

An intuitive, up-to-date introduction to random matrix theory and free calculus, with real world illustrations and Big Data applications.

A First Course in Computational Physics

A First Course in Computational Physics
Author: Paul L. DeVries
Publisher: Jones & Bartlett Publishers
Total Pages: 444
Release: 2011-01-28
Genre: Science
ISBN: 1449636195

Computers and computation are extremely important components of physics and should be integral parts of a physicist’s education. Furthermore, computational physics is reshaping the way calculations are made in all areas of physics. Intended for the physics and engineering students who have completed the introductory physics course, A First Course in Computational Physics, Second Edition covers the different types of computational problems using MATLAB with exercises developed around problems of physical interest. Topics such as root finding, Newton-Cotes integration, and ordinary differential equations are included and presented in the context of physics problems. A few topics rarely seen at this level such as computerized tomography, are also included. Within each chapter, the student is led from relatively elementary problems and simple numerical approaches through derivations of more complex and sophisticated methods, often culminating in the solution to problems of significant difficulty. The goal is to demonstrate how numerical methods are used to solve the problems that physicists face. Read the review published in Computing in Science & Engineering magazine, March/April 2011 (Vol. 13, No. 2) © 2011 IEEE, Published by the IEEE Computer Society