Advanced Mathematical Methods in Science and Engineering

A collection of an extensive range of mathematical topics into a plenary reference/textbook for solving mathematical and engineering problems. Topics covered include asymptotic methods, an explanation of Green's functions for ordinary and partial differential equations for unbounded and bounded media, and more.

Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology.

The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues.

The result reaches beyond nice mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry.

Booknews

This book breaks away from more theoretically burdensome texts, focusing on providing a set of useful tools that help readers understand the theoretical underpinnings of statistical methodology. Knight (statistics, U. of Toronto, Canada) emphasizes inferential procedures within the framework of parametric models and frequentist methodology, but also gives space to estimation from a non-parametric perspective and the Bayesian methods. Several sections also address computational issues, such as generating random variables, which are best suited for use with some type of statistical software. Annotation c. Book News, Inc., Portland, OR (booknews.com)

Applying Academic Skills To Practical Problems In Science And Engineering, Advanced Mathematical Methods In Science And Engineering Reviews Basic Methods Of Integration And Series Solutions For Ordinary Differential Equations ... Introduces Derivations And Solution Methods For Linear Boundary Value Problems In One Dimension, Covering Eigenfunctions And Eigenfunction Expansions, Orthogonality, And Adjoint And Self-adjoint Systems ... Discusses Complex Variables, Calculus, And Integrals; Application Of Residues; And The Integration Of Multivalued Functions ... Considers Linear Partial Differential Equations In Classical Physics And Engineering With Derivations For The Topics Of Wave Equations, Heat Flow, Vibration, And Strength Of Materials ... Clarifies The Calculus For Integral Transforms ... Facilitates The Use Of Integral Transforms With A Complete Treatment Of Complex Variables ... Explains Green's Functions For Ordinary And Partial Differential Equations For Unbounded And Bounded Media ... Examines Asymptotic Methods ... Presents Methods For Asymptotic Solutions Of Ordinary Differential Equations ... And More.--book Jacket. Ordinary Differential Equations -- Series Solutions Of Ordinary Differential Equations -- Special Functions -- Boundary Value Problems And Eigenvalue Problems -- Functions Of A Complex Variable -- Partial Differential Equations Of Mathematical Physics -- Integral Transforms -- Green's Functions -- Asymptotic Methods. S.i. Hayek. Includes Bibliographical References And Index. Traditional texts in mathematical statistics can seem - to some readers-heavily weighted with optimality theory of the various flavors developed in the 1940s and50s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow students to understand the theoretical underpinnings of statistical methodology. The author concentrates on inferential procedures within the framework of parametric models, but - acknowledging that models are often incorrectly specified - he also views estimation from a non-parametric perspective. Overall, Mathematical Statistics places greater emphasis on frequentist methodology than on Bayesian, but claims no particular superiority for that approach. It does emphasize, however, the utility of statistical and mathematical software packages, and includes several sections addressing computational issues. The result reaches beyond "nice" mathematics to provide a balanced, practical text that brings life and relevance to a subject so often perceived as irrelevant and dry. Features PREFACE......Page 5 TABLE OF CONTENTS......Page 8 1: ORDINARY DIFFERENTIAL EQUATIONS......Page 17 2: SERIES SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS......Page 34 3: SPECIAL FUNCTIONS......Page 58 4: BOUNDARY VALUE PROBLEMS AND EIGENVALUE PROBLEMS......Page 121 5: FUNCTIONS OF A COMPLEX VARIABLE......Page 199 6: PARTIAL DIFFERENTIAL EQUATIONS OF MATHEMATICAL PHYSICS......Page 306 7: INTEGRAL TRANSFORMS......Page 396 8: GREEN’S FUNCTIONS......Page 466 9: ASYMPTOTIC METHODS......Page 544 APPENDIX A INFINITE SERIES......Page 591 APPENDIX B SPECIAL FUNCTIONS......Page 605 APPENDIX C ORTHOGONAL COORDINATE SYSTEMS......Page 630 APPENDIX D DIRAC DELTA FUNCTIONS......Page 640 APPENDIX E PLOTS OF SPECIAL FUNCTIONS......Page 655 ANSWERS......Page 666 "Traditional texts in mathematical statistics can seem - to some readers - heavily weighted with optimality theory of the various flavours developed in the 1940s and 1950s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow readers to understand the theoretical underpinnings of statistical methodology."--BOOK JACKET. "The result is a balanced, practical text ideally suited for senior or graduate level studies in statistical theory."--BOOK JACKET. "Traditional texts in mathematical statistics can seem - to some readers - heavily weighted with optimality theory of the various flavours developed in the 1940s and 1950s, and not particularly relevant to statistical practice. Mathematical Statistics stands apart from these treatments. While mathematically rigorous, its focus is on providing a set of useful tools that allow readers to understand the theoretical underpinnings of statistical methodology." "The result is a balanced, practical text ideally suited for senior or graduate level studies in statistical theory."--Résumé de l'éditeur A linear ordinary differential equation is defined as one that relates a dependent variable, an independent variable and derivatives of the dependent variable with respect to the independent variable. In simple terms, a random experiment (or experiment) is a process whose outcome is uncertain.