Bøger af Fritz John

""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.

Interscience Tracts In Pure And Applied Mathematics, No. 2.

These Notes grew out of a course given by the author in 1952-53. Though the field of Partial Differential Equations has changed considerably since those days, particularly under the impact of methods taken from Functional Analysis, the author feels that the introductory material offered here still is basic for an understanding of the subject. It supplies the necessary intuitive foundation which motivates and anticipates abstract formulations of the questions and relates them to the description of natual phenomena. In the present edition, only minor corrections have been made in the text. An Index and up-to-date listing of books recommended for further study have been added. Fritz John New York November 19, 1970 v TABLE OF CONTENTS Introduetion 1 CHAPl'ER I - TEE SINGLE FIRST ORDER EQUATION 1. The linear and quasi-linear equations. 6 The general first order equation for a funetion 2. of two variables. * * * * * * * * * 15 The general first order equation for a funetion 3. of n independent variables. * * * * * 37 CHAPl'ER II - TEE CAUCIIT PROBLEM FOR HIGEER ORDER EQUATIONS 1. Analytie funetions of several real variables * Formulation of the Cauehy problem. The not ion 2. of eharaeteristies. * * * 54 3. The Cauehy problem for the general non-linear equation. 71 4. The Cauehy-Kowalewsky theorem. 76 CHAPl'ER 111 - SECOND ORDER EQUATIONS WITH CONSTANT COEFFICIENTS 1. Equations in two independent variables.

This book is a very well-accepted introduction to the subject. Now, in this fourth edition, the book has again been updated with an additional chapter on Lewy's example of a linear equation without solutions.

From the Preface: (...) The book is addressed to students on various levels, to mathematicians, scientists, engineers. Instead of obstructing the access to the wealth of facts by lengthy discussions of a fundamental nature we have sometimes postponed such discussions to appendices in the various chapters.

From the reviews: "...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: "...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