An Introduction to the Study of Integral Equations (Classic Reprint)

Explore the foundations and methods of integral equations, a cornerstone of mathematical analysis.

This classic reference lays out the theory behind integral equations and their major uses in mechanics and physics, with clear development from definitions to solution techniques for the linear first and second kinds.

The book frames the subject’s history, key problems, and essential tools. It emphasizes how integral equations relate to, yet differ from, differential equations, and shows how simple, single-integral problems can reveal powerful techniques applicable to more complex cases. You will find carefully chosen theorems, practical approaches to kernels and determinants, and a focus on continuous solutions and their properties.
What you’ll experience

• Core concepts: what integral equations are, and how they arise from physical problems.
• Fundamental methods: how to formulate, analyze, and solve linear integral equations of the first and second kinds.
• Toolset for kernels: handling kernels, regular distributions of discontinuities, and modified determinants.
• Step-by-step reasoning: detailed theorems and their proofs to build a solid mathematical intuition.

Ideal for students, researchers, and practitioners seeking a rigorous introduction to integral equations and their applications in analysis and physics.

First published in 1914, this book was written to provide readers with 'the main portions of the theory of integral equations in a readable and, at the same time, accurate form, following roughly the lines of historical development'. Textual notes are incorporated throughout.