Suitable for advanced undergraduate and graduate students, this text presents the general properties of partial differential equations, including the elementary theory of complex variables. Solutions. 1965 edition.
Handy compilation of 100 practice problems, hints, and solutions indispensable for students preparing for the William Lowell Putnam and other mathematical competitions. Problems suggested by a variety of sources: Crux Mathematicorum, Mathematics Magazine, The American Mathematical Monthly and others. Preface to the First Edition. Sources. 1988 edition.
This volume introduces the basic mathematical tools behind conformal mapping, describes advances in technique, and illustrates a broad range of applications. 1991 edition. Includes 247 figures and 38 tables.
This book arose out of the authors' desire to present Lebesgue integration and Fourier series on an undergraduate level, since most undergraduate texts do not cover this material or do so in a cursory way. The result is a clear, concise, well-organized introduction to such topics as the Riemann integral, measurable sets, properties of measurable sets, measurable functions, the Lebesgue integral, convergence and the Lebesgue integral, pointwise convergence of Fourier series and other subjects. The authors not only cover these topics in a useful and thorough way, they have taken pains to motivate the student by keeping the goals of the theory always in sight, justifying each step of the development in terms of those goals. In addition, whenever possible, new concepts are related to concepts already in the student's repertoire. Finally, to enable readers to test their grasp of the material, the text is supplemented by numerous examples and exercises. Mathematics students as well as students of engineering and science will find here a superb treatment, carefully thought out and well presented , that is ideal for a one semester course. The only prerequisite is a basic knowledge of advanced calculus, including the notions of compactness, continuity, uniform convergence and Riemann integration.
This text offers students in mathematics, engineering, and the applied sciences a solid foundation for advanced studies in mathematics. Features coverage of integral equations and basic scattering theory. Includes exercises, many with answers. 1988 edition.
Uniquely provides fully solved problems for linear partial differential equations and boundary value problems Partial Differential Equations: Theory and Completely Solved Problems utilizes real-world physical models alongside essential theoretical concepts. With extensive examples, the book guides readers through the use of Partial Differential Equations (PDEs) for successfully solving and modeling phenomena in engineering, biology, and the applied sciences. The book focuses exclusively on linear PDEs and how they can be solved using the separation of variables technique. The authors begin by describing functions and their partial derivatives while also defining the concepts of elliptic, parabolic, and hyperbolic PDEs. Following an introduction to basic theory, subsequent chapters explore key topics including: • Classification of second-order linear PDEs • Derivation of heat, wave, and Laplace’s equations • Fourier series • Separation of variables • Sturm-Liouville theory • Fourier transforms Each chapter concludes with summaries that outline key concepts. Readers are provided the opportunity to test their comprehension of the presented material through numerous problems, ranked by their level of complexity, and a related website features supplemental data and resources. Extensively class-tested to ensure an accessible presentation, Partial Differential Equations is an excellent book for engineering, mathematics, and applied science courses on the topic at the upper-undergraduate and graduate levels.
A survey of Euclid's Elements, this text provides an understanding of the classical Greek conception of mathematics. It offers a well-rounded perspective, examining similarities to modern views as well as differences. Rather than focusing strictly on historical and mathematical issues, the book examines philosophical, foundational, and logical questions. Although comprehensive in its treatment, this study represents a less cumbersome, more streamlined approach than the classic three-volume reference by Sir Thomas L. Heath (also available from Dover Publications). To make reading easier and to facilitate access to individual analyses and discussions, the author has included helpful appendixes. These list special symbols and additional propositions, along with all of the assumptions and propositions of the Elements and notations of their discussion within this volume.
This text provides an introduction to partial differential equations and boundary value problems, including Fourier series. The treatment offers students a smooth transition from a course in elementary ordinary differential equations to more advanced topics in a first course in partial differential equations. This widely adopted and successful book also serves as a valuable reference for engineers and other professionals. The approach emphasizes applications, with particular stress on physics and engineering applications. Rich in proofs and examples, the treatment features many exercises in each section. Relevant Mathematica files are available for download from author Nakhlé Asmar's website; however, the book is completely usable without computer access. The Students' Solutions Manual can be downloaded for free from the Dover website, and the Instructor's Solutions Manual is available upon request for professors and potential teachers. The text is suitable for undergraduates in mathematics, physics, engineering, and other fields who have completed a course in ordinary differential equations.
'Modelling with Differential Equations in Chemical Engineering' covers the modelling of rate processes of engineering in terms of differential equations. While it includes the purely mathematical aspects of the solution of differential equations, the main emphasis is on the derivation and solution of major equations of engineering and applied science. Methods of solving differential equations by analytical and numerical means are presented in detail with many solved examples, and problems for solution by the reader. Emphasis is placed on numerical and computer methods of solution. A key chapter in the book is devoted to the principles of mathematical modelling. These principles are applied to the equations in important engineering areas. The major disciplines covered are thermodynamics, diffusion and mass transfer, heat transfer, fluid dynamics, chemical reactions, and automatic control. These topics are of particular value to chemical engineers, but also are of interest to mechanical, civil, and environmental engineers, as well as applied scientists. The material is also suitable for undergraduate and beginning graduate students, as well as for review by practising engineers.
This concrete approach to harmonic analysis begins with the circle group T and deals with classical Fourier series in the first five chapters, turning to the real line in chapter six, locally compact abelian groups in chapter seven, and commutative Banach algebras in final chapter.
With this book, even readers unfamiliar with the field can acquire sufficient background to understand research literature related to the theory of parabolic and elliptic equations. 1964 edition.
Algebraically based approach to vectors, mapping, diffraction, and other topics in applied math also covers generalized functions, analytic function theory, and more. Additional topics include sections on linear algebra, Hilbert spaces, calculus of variations, boundary value problems, integral equations, analytic function theory, and integral transform methods. Exercises. 1969 edition.
Dieses Buch ist eine umfassende Einführung in die klassischen Lösungsmethoden partieller Differentialgleichungen. Es wendet sich an Leser mit Kenntnissen aus einem viersemestrigen Grundstudium der Mathematik (und Physik) und legt seinen Schwerpunkt auf die explizite Darstellung der Lösungen. Es ist deshalb besonders auch für Anwender (Physiker, Ingenieure) sowie für Nichtspezialisten, die die Methoden der mathematischen Physik kennenlernen wollen, interessant. Durch die große Anzahl von Beispielen und Übungsaufgaben eignet es sich gut zum Gebrauch neben Vorlesungen sowie zum Selbststudium.
Fundamentals of analytic function theory -- plus lucid exposition of 5 important applications: potential theory, ordinary differential equations, Fourier transforms, Laplace transforms, and asymptotic expansions. Includes 66 figures.
Suitable for advanced courses in applied mathematics, this text covers analysis of lumped parameter systems, distributed parameter systems, and important areas of applied mathematics. Answers to selected problems. 1970 edition.