Kirjahaku

The mathematical works of Fritz John whose deep and original ideas have had a great influence on the development of various fields in mathema tical analysis are made available with these volumes. His works are certainly well known to the experts, but knowledge of his contributions may not have spread as widely as it should have. For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the publication of this collection, a wider circle of mathematicians will become familiar with, and appreciate, the fertile ideas of Fritz John. The organization of these two volumes was undertaken in consultation with the author. It was decided not to present the papers in chronological order, but rather to subdivide them into ten sections representing different mathematical topics to which John has contributed. Commentaries made by experts in the fields are appended to each section. Since the division into sec tions could, of course, not be made sharply, there are several overlaps. For instance, the comments of Louis Nirenberg refer to Elasticity Theory VI, Geometric Inequalities VIII, and Functions of Bounded Mean Oscillations IX. To help the reader, cross-references and remarks by the author will be found at the end of each section."

The mathematical works of Fritz John whose deep and original ideas have had a great influence on the development of various fields in mathema­ tical analysis are made available with these volumes. His works are certainly well known to the experts, but knowledge of his contributions may not have spread as widely as it should have. For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the publication of this collection, a wider circle of mathematicians will become familiar with, and appreciate, the fertile ideas of Fritz John. The organization of these two volumes was undertaken in consultation with the author. It was decided not to present the papers in chronological order, but rather to subdivide them into ten sections representing different mathematical topics to which John has contributed. Commentaries made by experts in the fields are appended to each section. Since the division into sec­ tions could, of course, not be made sharply, there are several overlaps. For instance, the comments of Louis Nirenberg refer to Elasticity Theory VI, Geometric Inequalities VIII, and Functions of Bounded Mean Oscillations IX. To help the reader, cross-references and remarks by the author will be found at the end of each section.

The mathematical works of Fritz John whose deep and original ideas have had a great influence on the development of various fields in mathema­ tical analysis are made available with these volumes. His works are certainly well known to the experts, but knowledge of his contributions may not have spread as widely as it should have. For example, the concept of functions of bounded mean oscillations plays a central role in harmonic analysis today, but it is perhaps less known that this class of functions was introduced by John as early as 1961, motivated by his work in elasticity theory. With the publication of this collection, a wider circle of mathematicians will become familiar with, and appreciate, the fertile ideas of Fritz John. The organization of these two volumes was undertaken in consultation with the author. It was decided not to present the papers in chronological order, but rather to subdivide them into ten sections representing different mathematical topics to which John has contributed. Commentaries made by experts in the fields are appended to each section. Since the division into sec­ tions could, of course, not be made sharply, there are several overlaps. For instance, the comments of Louis Nirenberg refer to Elasticity Theory VI, Geometric Inequalities VIII, and Functions of Bounded Mean Oscillations IX. To help the reader, cross-references and remarks by the author will be found at the end of each section.

From the reviews of the earlier editions: “An excellent second-reading text. Should be accessible to any mathematician. Highly recommended.” – The Mathematical Gazette “An excellent text upon which to build and introduction to partial differential equations at the graduate level. In addition…recommended for the nonspecialist.” – American Mathematical Monthly Partial Differential Equations is a very well accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy’s example of a linear equation with solutions.

""Plane Waves And Spherical Means: Applied To Partial Differential Equations"" by John, Fritz is a comprehensive guide to the application of plane waves and spherical means in solving partial differential equations. The book covers a wide range of topics, including the theory of Fourier series and integrals, the Laplace and Poisson equations, and the wave equation. It also provides an introduction to the theory of distributions and the use of Green's functions in solving boundary value problems. The book is written in a clear and concise style, making it accessible to both graduate students and researchers in mathematics and physics. It includes numerous examples and exercises to help readers develop their understanding of the material. Overall, ""Plane Waves And Spherical Means: Applied To Partial Differential Equations"" is an essential resource for anyone interested in the application of mathematical methods to the study of physical phenomena.Interscience Tracts In Pure And Applied Mathematics, No. 2.This scarce antiquarian book is a facsimile reprint of the old original and may contain some imperfections such as library marks and notations. Because we believe this work is culturally important, we have made it available as part of our commitment for protecting, preserving, and promoting the world's literature in affordable, high quality, modern editions, that are true to their original work.

From the reviews of the earlier editions: “An excellent second-reading text. Should be accessible to any mathematician. Highly recommended.” – The Mathematical Gazette “An excellent text upon which to build and introduction to partial differential equations at the graduate level. In addition…recommended for the nonspecialist.” – American Mathematical Monthly Partial Differential Equations is a very well accepted introduction to the subject. In it, the author identifies the significant aspects of the theory and explores them with a limited amount of machinery from mathematical analysis. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy’s example of a linear equation with solutions.

Joan - A novel. Vol. 1 is an unchanged, high-quality reprint of the original edition of 1796. Hansebooks is editor of the literature on different topic areas such as research and science, travel and expeditions, cooking and nutrition, medicine, and other genres. As a publisher we focus on the preservation of historical literature. Many works of historical writers and scientists are available today as antiques only. Hansebooks newly publishes these books and contributes to the preservation of literature which has become rare and historical knowledge for the future.

From the reviews: "Volume 1 covers a basic course in real analysis of one variable and Fourier series. It is well-illustrated, well-motivated and very well-provided with a multitude of unusually useful and accessible exercises. (...) There are three aspects of Courant and John in which it outshines (some) contemporaries: (i) the extensive historical references, (ii) the chapter on numerical methods, and (iii) the two chapters on physics and geometry. The exercises in Courant and John are put together purposefully, and either look numerically interesting, or are intuitively significant, or lead to applications. It is the best text known to the reviewer for anyone trying to make an analysis course less abstract. (...)" The Mathematical Gazette (75.1991.471)

From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that."Newsletter on Computational and Applied Mathematics, 1991"...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students." Acta Scientiarum Mathematicarum, 1991

From the reviews: "These books (Introduction to Calculus and Analysis Vol. I/II) are very well written. The mathematics are rigorous but the many examples that are given and the applications that are treated make the books extremely readable and the arguments easy to understand. These books are ideally suited for an undergraduate calculus course. Each chapter is followed by a number of interesting exercises. More difficult parts are marked with an asterisk. There are many illuminating figures...Of interest to students, mathematicians, scientists and engineers. Even more than that."Newsletter on Computational and Applied Mathematics, 1991"...one of the best textbooks introducing several generations of mathematicians to higher mathematics. ... This excellent book is highly recommended both to instructors and students.Acta Scientiarum Mathematicarum, 1991

The description for this book, Contributions to the Theory of Partial Differential Equations. (AM-33), will be forthcoming.