Product Integration with Application to Differential Equations [Hardcover]

This 1979 book shows how differential equation theory can be beautifully simplified by treating such equations from the product integral viewpoint.This 1979 book shows how differential equation theory can be beautifully simplified by treating such equations from the product integral viewpoint. The first chapter, dealing with linear ordinary differential equations, is accessible to anyone with a knowledge of matrix theory and elementary calculus. Later chapters assume a more sophisticated reader.This 1979 book shows how differential equation theory can be beautifully simplified by treating such equations from the product integral viewpoint. The first chapter, dealing with linear ordinary differential equations, is accessible to anyone with a knowledge of matrix theory and elementary calculus. Later chapters assume a more sophisticated reader.Originally published in 1979, this book shows the beautiful simplifications that can be brought to the theory of differential equations by treating such equations from the product integral viewpoint. The first chapter of the book, dealing with linear ordinary differential equations, should be accessible to anyone with a knowledge of matrix theory and elementary calculus. Later chapters assume more sophistication on the part of the reader. The essential unity of these subjects is illustrated by the fact that the idea of the product integral can be naturally and effectively used to deal with all of them.Editor's statement; Section editor's statement; Preface; 1. Product integration of matrix-valued functions; 2. Contour product integration; 3. Strong product integration; 4. Applications; 5. Product integration of measures; 6. Complements; other work and further results on product integration; Appendices; References; Notes to the references.Review of the hardback: 'This book is an attractive, elementary introduction to the product integral and includes a general survey of the subject by P. R. Masani'. American Mathematical Monthly