[pdf] Variational, Topological, And Partial Order Methods With Their Applications (developments in Mathematics, Vol. 29)

Understanding special sets of integers was classically of interest to Hadamard, Zygmund and others, and continues to be of interest today. This book is a modern treatment of the subject of interpolation and Sidon sets.

Although the calculus of variations has ancient origins in questions of Ar­ istotle and Zenodoros, its mathematical principles first emerged in the post­ calculus investigations of Newton, the Bernoullis, Euler, and Lagrange. Its results now supply fundamental tools of exploration to both mathematicians and those in the applied sciences. (Indeed, the macroscopic statements ob­ tained through variational principles may provide the only valid mathemati­ cal formulations of many physical laws. ) Because of its classical origins, variational calculus retains the spirit of natural philosophy common to most mathematical investigations prior to this century.

In this undergraduate/graduate textbook, the authors introduce ODEs and PDEs through 50 class-tested lectures. Mathematical concepts are explained with clarity and rigor, using fully worked-out examples and helpful illustrations. Exercises are provided at the end of each chapter for practice.

Clear and concise introduction to matrices with elegant proofs; Of interest to scientists from many disciplines; Gives many interesting applications to different parts of mathematics, such as algebra, analysis and complexity theory; Contains 160 exercises, half of them on advanced material; Includes at least one advanced result per chapter