A First Course on Orthogonal Polynomials

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

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

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"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"--

A First Course in Numerical Analysis

A First Course in Numerical Analysis
Title A First Course in Numerical Analysis PDF eBook
Author Anthony Ralston
Publisher Courier Corporation
Pages 644
Release 2001-01-01
Genre Mathematics
ISBN 9780486414546

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Outstanding text, oriented toward computer solutions, stresses errors in methods and computational efficiency. Problems — some strictly mathematical, others requiring a computer — appear at the end of each chapter.

Fourier Series and Orthogonal Polynomials

Fourier Series and Orthogonal Polynomials
Title Fourier Series and Orthogonal Polynomials PDF eBook
Author Dunham Jackson
Publisher American Mathematical Soc.
Pages 249
Release 1941-12-31
Genre Fourier series
ISBN 1614440069

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The underlying theme of this monograph is that the fundamental simplicity of the properties of orthogonal functions and the developments in series associated with them makes those functions important areas of study for students of both pure and applied mathematics. The book starts with Fourier series and goes on to Legendre polynomials and Bessel functions. Jackson considers a variety of boundary value problems using Fourier series and Laplace's equation. Chapter VI is an overview of Pearson frequency functions. Chapters on orthogonal, Jacobi, Hermite, and Laguerre functions follow. The final chapter deals with convergence. There is a set of exercises and a bibliography. For the reading of most of the book, no specific preparation is required beyond a first course in the calculus. A certain amount of “mathematical maturity” is presupposed or should be acquired in the course of the reading.

A First Course in Numerical Methods

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

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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
Title A First Course in the Numerical Analysis of Differential Equations PDF eBook
Author A. Iserles
Publisher Cambridge University Press
Pages 402
Release 1996-01-18
Genre Mathematics
ISBN 9780521556552

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Numerical analysis presents different faces to the world. For mathematicians it is a bona fide mathematical theory with an applicable flavour. For scientists and engineers it is a practical, applied subject, part of the standard repertoire of modelling techniques. For computer scientists it is a theory on the interplay of computer architecture and algorithms for real-number calculations. The tension between these standpoints is the driving force of this book, which presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance between theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics. Dr Iserles concentrates on fundamentals: deriving methods from first principles, analysing them with a variety of mathematical techniques and occasionally discussing questions of implementation and applications. By doing so, he is able to lead the reader to 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.

A First Course in the Design of Experiments

A First Course in the Design of Experiments
Title A First Course in the Design of Experiments PDF eBook
Author John H. Skillings
Publisher Routledge
Pages 700
Release 2018-05-08
Genre Mathematics
ISBN 1351469967

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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.