دانلود کتاب Introduction to the Theory of Partial Differential Equations

This one-year course is written on classical lines with a slant towards modern methods. It will meet the requirements of senior honours under- graduates and postgraduates who require a systematic introductory text outlining the theory of partial differential equations. The amount of theory presented will meet the needs of most theoretical scientists, and pure mathe- maticians will find here a sound basis for the study of recent advances in the subject.Clear exposition of the elementary theory is a key feature of the book, and the treatment is rigorous. The author begins by outlining some of the more common equations of mathematical physics. He then discusses the principles involved in the solution of various types of partial differential equation. A close study of the existence and uniqueness theorem is reinforced by proof. Second-order equations, because of their significance, are considered in detail. Dr. Smith's approach to the analysis is traditional, but by intro- ducing the concept of generalized functions and demonstrating their relevance, he helps the reader to gain a better understanding of Hadamard's theory and to pass painlessly on to the more difficult works by Courant and Hormander. The text is reinforced by many worked examples, and problems for solution have been included where appropriate.