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2 chapter 1PhysicsCPFigure 1.1 A representation of the multidisciplinary nature of computational physics both asan overlap of physics, applied mathematics, and computer science and as a bridge amongthe disciplines.Although related, computational science is not computer science. Computer sciencestudies computing for its own intrinsic interest and develops the hardware andsoftware tools that computational scientists use. Likewise, applied mathematicsdevelops and studies the algorithms that computational scientists use. As much aswe too find math and computer science interesting for their own sakes, our focus ison solving physical problems; we need to understand the CS and math tools wellenough to be able to solve our problems correctly.As CP has matured, we have come to realize that it is more than the overlapof physics, computer science, and mathematics (Figure 1.1). It is also a bridgeamong them (the central region in Figure 1.1) containing core elements of it own,such as computational tools and methods. To us, CP’s commonality of tools and aproblem-solving mindset draws it toward the other computational sciences andaway from the subspecialization found in so much of physics.In order to emphasize our computational science focus, to the extent possible,we present the subjects in this book in the form of a problem to solve, withthe components that constitute the solution separated according to the scientificproblem-solving paradigm (Figure 1.2 left). Traditionally, physics employs bothexperimental and theoretical approaches to discover scientific truth (Figure 1.2right). Being able to transform a theory into an algorithm requires significanttheoretical insight, detailed physical and mathematical understanding, and amastery of the art of programming. The actual debugging, testing, and organizationof scientific programs is analogous to experimentation, with the numericalsimulations of nature being essentially virtual experiments. The synthesis of−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 2