What is "Introduction to Integral Equations with Applications"?
Jerri details several analytical and numerical techniques to solve these equations. An integral equation is any equation where the
Jerri’s book categorizes integral equations into logical, manageable frameworks. An integral equation is any equation where the unknown function appears under an integral sign. 1. Fredholm Integral Equations You will learn the differences between: | Chapter
Jerri begins with the fundamentals. You will learn the differences between: Banach fixed point theorem (contraction mapping)
| Chapter / Section | Core Topics Covered | | :--- | :--- | | | Introduction to how integral equations arise from physics and engineering; classification (Fredholm vs. Volterra, first vs. second kind, singular); basic mathematical tools. | | 2. Modeling of Problems as Integral Equations | Converting real-world problems (e.g., in mechanics, electrical engineering) into integral equation form; examples from various fields. | | 3. Volterra Integral Equations | Detailed study of Volterra equations; solution methods including Laplace transforms, series solutions, and successive approximations. | | 4. The Green's Function | Representation of boundary value problems via Green's functions; construction and application for solving differential equations. | | 5. Fredholm Integral Equations | Core of the book—methods for Fredholm equations; degenerate (separable) kernels, iterative methods; distinction between first and second kind. | | 6. Existence of Solutions: Basic Fixed Point Theorems | Theoretical underpinnings; Banach fixed point theorem (contraction mapping); establishing conditions for unique solutions. | | 7. Higher Quadrature Rules for the Numerical Solutions | New to 2nd edition! Practical numerical methods for solving integral equations; Newton-Cotes, Gaussian quadrature, and their application to integral equations. | | Appendices | Fourier and Hankel transforms; Green's function solutions to classic boundary value problems; advanced applications in PDEs. | | Back Matter | Answers to selected exercises; comprehensive bibliography; detailed index. |