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【資源】Computational Physics - M. Jensen
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Computational Physics - M. Jensen COMPUTATIONAL PHYSICS M. Hjorth-Jensen In the physical sciences we often encounter problems of evaluating various properties of a given function f(x). Typical operations are differentiation, integration and finding the roots of f(x). In most cases we do not have an analytical expression for the function f(x) and we cannot derive explicit formulae for derivatives etc. Even if an analytical expression is available, the evaluation of certain operations on f(x) are so difficult that we need to resort to a numerical evaluation. More frequently, f(x) is the result of complicated numerical operations and is thus known only at a set of discrete points and needs to be approximated by some numerical methods in order to obtain derivatives, etc etc. The aim of these lecture notes is to give you an introduction to selected numerical meth- ods which are encountered in the physical sciences. Several examples, with varying degrees of complexity, will be used in order to illustrate the application of these methods. The text gives a survey over some of the most used methods in Computational Physics and each chapter ends with one or more applications to realistic systems, from the structure of a neu- tron star to the description of few-body systems through Monte-Carlo methods. Several minor exercises of a more numerical character are scattered throughout the main text. The topics we cover start with an introduction to C/C++ and Fortran 90/95 programming combining it with a discussion on numerical precision, a point we feel is often neglected in com- putational science. This chapter serves also as input to our discussion on numerical derivation in chapter 3. In that chapter we introduce several programming concepts such as dynamical mem- ory allocation and call by reference and value. Several program examples are presented in this chapter. For those who choose to program in C/C++ we give also an introduction to the auxiliary library Blitz++, which contains several useful classes for numerical operations on vectors and matrices. The link to Blitz++, matrices and selected algorithms for linear algebra problems are dealt with in chapter 5. Chapters 6 and 7 deal with the solution of non-linear equations and the finding of roots of polynomials and numerical interpolation, extrapolation and data fitting. Therafter we switch to numerical integration for integrals with few dimensions, typically less than 3, in chapter 8. The numerical integration chapter serves also to justify the introduction of Monte-Carlo methods discussed in chapters 9 and 10. There, a variety of applications are presented, from integration of multidimensional integrals to problems in statistical Physics such as random walks and the derivation of the diffusion equation from Brownian motion. Chapter》》》》》》》》》》》》 http://d.namipan.com/d/7ad34a6e1 ... 66fea92bccbf9b02600 http://d.namipan.com/d/7ad34a6e1 ... 66fea92bccbf9b02600 http://d.namipan.com/d/7ad34a6e162e7102cd438dccde74d66fea92bccbf9b02600 |
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