A First Course in Integral Equations

Abstract

Within the last eighteen years since the publication of the first edition of A First Course in Integral Equations, the growth in the field of Integral Equations has been flourishing with many advances. The new developments, which complement the traditional concepts, present clear expositions of the main concepts and keys of Integral Equations. Moreover, a further significant recognition of the use of Integral Equations in scientific fields, engineering, and mathematics has developed. This recognition has been followed up with further achievements in research. Like the first edition, the second edition is helpful to a wide range of advanced undergraduate and graduate students in varying fields, as well as researchers in science, mathematics, and engineering. Some of the strengths of the new edition are the detailed treatments, clarifications, explanations of the new developments, discussions of the wide variety of examples, and the wellpresented illustrations to aid the learner to better understand the concepts. In editing this new edition, the following distinguishing features, above the pedagogical aims of the first edition, were highly considered: 1. Many new and remarkable developments have been added. The scope of each chapter is extended to contain these fascinating new findings. 2. The linear and the nonlinear integral equations were handled in a systematic manner with more methods and applications. This edition provides very systematic and detailed instructions on how to handle each kind of equations. 3. Many people have written to me since the publication of the first edition. They offered many useful and constructive suggestions. Their suggestions for extending some topics were honored in this text. 4. The fruitful evaluations, made by my students who used the first edition, provide useful input. My students’ questions and concerns were addressed in this edition. 5. A new application chapter has been added to discuss a variety of scientific applications. Numerical and analytic treatments of linear and nonlinear integral equations are explained in this chapter to highlight the effectiveness of the traditional