Green's Functions [Paperback]

Second edition of a work first published in 1980 by van Nostrand. Intended to be a self-contained and systematic introduction to the theory of Green's functions and the general ideas involved in their application to differential equations. Applicability rather than rigor is the author's main concern.Second edition of a work first published in 1980 by van Nostrand. Intended to be a self-contained and systematic introduction to the theory of Green's functions and the general ideas involved in their application to differential equations. Applicability rather than rigor is the author's main concern.Green's functions are an important tool used in solving boundary value problems associated with ordinary and partial differential equations. This self-contained and systematic introduction to Green's functions has been written with applications in mind. The material is presented in an unsophisticated and rather more practical manner than usual. Consequently advanced undergraduates and beginning postgraduate students in mathematics and the applied sciences will find this account particularly attractive. Many exercises and examples have been supplied throughout to reinforce comprehension and to increase familiarity with the technique.Preface; Part I. The Concept of a Green's Function; Part II. Vector Spaces and Linear Transformations; Part III. Systems of Finite Dimension; Part IV. Continuous Functions; Part V. Integral Operators; Part VI. Generalized Fourier Series and Complete Vector Spaces; Part VII. Differential Operators; Part VIII. Integral Equations; Part IX. Green's Functions in Higher-Dimensional Spaces; Part X. Calculation of Particular Green's Functions; Part XI. Approximate Green's Functions; Appendices; Bibliography; Chapter references; Index.'It is well planned and splendidly motivated and the computational material is covered without obscuring the conceptual development.' Bulletin of the Institute of Mathematics and its Applications'The exposition is generally cllÃ