ELEMENTS OF APPLIED MATHEMATICS - YA.B. ZELDOVICH, A.D. MYSKIS

This book is not a textbook in the ordinary sense of the word but rather a reader in the mathematical sciences. Using simple examples taken from physics and a variety of mathematical problems, we have tried to introduce the reader to a broad range of ideas and methods that are found in present-day applications of mathematics to physics, engineering and other fields. Some of these ideas and methods (such as the use of the delta function, the principle of superposition, obtaining asymptotic expressions, etc.) have not been sufficiently discussed in the ordinary run of mathematics textbooks for non-mathematicians, and so this text can serve as a supplement to such textbooks.
Our aim has been to elucidate the basic ideas of mathematical methods and the general laws of the phenomena at hand. Formal proofs, exceptions and complicating factors have for the most part been dropped.
Instead we have strived in certain places to go deeper into the physical picture of the processes.
It is assumed that the reader has a grasp of the basic essentials of differential and integral calculus for functions of one variable, including the expansion of such functions in power series, and is able to use such knowledge in the solution of physical problems. It is sufficient (but not necessary!) to be acquainted with Zeldovich's Higher Mathematics for Beginners (Mir Publishers, Moscow, 1973), which we will refer to throughout this text as HM. What is more, the present text may be regarded as a continuation of Higher Mathematics for Beginners. In some places the material is closely related to Myškis Lectures in Higher Mathematics (Mir Publishers, Moscow, 1972).
Nevertheless, this text is completely independent and requires of the reader only the background indicated above. Nothing else.
The range of this book is clear from the table of contents. The reader need not study it chapter by chapter but may, in accordance with his particular interests, dip into any chapter, taking care to follow up any references to other sections of the book.