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[资源] 【资源】Computational Physics - M. Jensen

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》》》》》》》》》》》》

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