A comprehensive book on Applied Mathematics for beginners The Princeton Companion To Mathematics is described on Wikipedia thus:

The book concentrates primarily on modern pure mathematics rather than applied mathematics, although it does also cover both applications of mathematics and the mathematics that relates to those applications; it provides a broad overview of the significant ideas and developments in research mathematics. It is organized into eight parts:

Although this book includes Applied Mathematics, can any one recommend a comprehensive beginners book on Applied Mathematics ?
 A: I'd like to expand a little on @lhf's comment recommending Introduction to Applied Mathematics by Gilbert Strang. Whether it is appropriate for beginners depends on your precise definition of beginner - I would recommend background in linear algebra, multivariable calculus and differential equations at the very least before reading it. Where it excels is in setting up and introducing a unified framework for a large swath of applied mathematics based on equilibrium equations and minimum principles (see chapters 1-3, especially chapter 2). The table of contents can be found at http://www-math.mit.edu/~gs/books/itam_toc.html. The topics cover much of traditional and contemporary applied mathematics, including optimization. However, the book makes no claims to being encyclopedic. 
See also Strang's more recent Computational Science and Engineering. There's a table of contents for this book at http://math.mit.edu/~gs/cse/.
A: Applied Mathematics for Engineers and Physicists by Louis A. Pipes and Lawrence R. Harvill
Amazon.com quote:

One of the most widely used reference books on applied mathematics for
  a generation, distributed in multiple languages throughout the world,
  this text is geared toward use with a one-year advanced course in
  applied mathematics for engineering students. The treatment assumes a
  solid background in the theory of complex variables and a familiarity
  with complex numbers, but it includes a brief review. Chapters are as
  self-contained as possible, offering instructors flexibility in
  designing their own courses. The first eight chapters explore the
  analysis of lumped parameter systems. Succeeding topics include
  distributed parameter systems and important areas of applied
  mathematics. Each chapter features extensive references for further
  study as well as challenging problem sets. Answers and hints to select
  problem sets are included in an Appendix. This edition includes a new
  Preface by Dr. Lawrence R. Harvill.

