Título: Introduction to Non-linear Differential and Integral Equations
Autor: Harold Thayer Davis
Sinopse: Within recent years interest in nonlinear equations has grown enormously. They are extremely important as basic equations in many areas of mathematical physics, and they have received renewed attention because of progress in their solution by machines. This volume undertakes a definition of the field, indicating advances that have been made up through 1960. The author's position is that while the advent of machines has resulted in much new knowledge, one should not disregard analytical methods, since the solution of nonlinear equations possesses singularities which only the analytical method (as based upon the work of Poincare, Liapounoff, Painleve and Goursatl can discover. After a general survey of the problem presented by nonlinear equations, the author discusses the differential equation of the first order, following this by chapters on the Riccati equation (as a bridge between linear and nonlinear equations) and existence theorems, with special reference to Cauchy's method. Second order equations are introduced via Volterra's problem and the problem of pursuit, and succeeding chapters cover elliptic integrals and functions and theta functions; differential equations of the second order; and second order differential equations of the polynomial class, with special reference to Painleve transcendents. The technique of continuous analytical continuation is shown, while phenomena of the phase plane are studied as an introduction to nonlinear mechanics. Nonlinear 111echanics is then discussed, with various classical equations like Van der Pol's equations, Emden's equation, and the Duffing problem. The remaining chapters are concerned with nonlinear integral equations, problems from the calculus of variations, and numerical integration of nonlinear equations. Throughout the book the results of distinguished analysis of the past and modern machine computations are both taken into account. Despite the thoroughness of its coverage this is a very fine introduction to this important area of mathematics, and it can easily be followed by the mathematically sophisticated reader who knows very little about nonlinear equations.
Contexto da obra
Quando a classificação é mais ampla, o contexto do livro costuma depender ainda mais de autoria, tema e edição. “Introduction to Non-linear Differential and Integral Equations”, de Harold Thayer Davis, publicado pela editora Dover Publications Inc., em 1960 e com 566 páginas, integra a categoria Livros Variados. Por isso, autoria, edição e tema acabam tendo ainda mais peso na forma de apresentar o livro.
Editora: Dover Publications Inc.
Páginas: 566
Ano: 1960
Edição: F First Edition
Linguagem: pt_BR
ISBN: 9780486609713
ISBN13: 9780486609713
Sobre a editora
Os livros da editora Dover Publications Inc. apresentam uma variedade de temas que transitam entre ciências exatas, artes visuais e literatura clássica. A experiência de leitura frequentemente envolve um mergulho detalhado em assuntos específicos, como a história da química, técnicas artísticas tradicionais ou coleções de contos e ensaios. O tom das obras varia do didático e técnico ao narrativo e ilustrativo, com muitos volumes oferecendo explicações claras, ilustrações precisas e contextualizações históricas. O catálogo sugere uma preferência por textos que combinam rigor informativo com acessibilidade, contemplando desde guias práticos para desenhistas até compilações literárias que exploram aspectos culturais e históricos.
