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[资源] 经典物理书籍：计算物理学的基本概念（Basic Concepts in Computational Physics）

Basic Concepts in Computational Physics

With the development of ever more powerful computers a new branch of physics and engineering evolved over the last few decades: Computer Simulation or Computational Physics. It serves two main purposes:
- Solution of complex mathematical problems such as, differential equations, minimization/optimization, or high-dimensional sums/integrals.
- Direct simulation of physical processes, as for instance, molecular dynamics or Monte-Carlo simulation of physical/chemical/technical processes.
Consequently, the book is divided into two main parts: Deterministic methods and stochastic methods. Based on concrete problems, the first part discusses numerical differentiation and integration, and the treatment of ordinary differential equations. This is augmented by notes on the numerics of partial differential equations. The second part discusses the generation of random numbers, summarizes the basics of stochastics which is then followed by the introduction of various Monte-Carlo (MC) methods. Specific emphasis is on MARKOV chain MC algorithms. All this is again augmented by numerous applications from physics. The final two chapters on Data Analysis and Stochastic Optimization share the two main topics as a common denominator. The book offers a number of appendices to provide the reader with more detailed information on various topics discussed in the main part. Nevertheless, the reader should be familiar with the most important concepts of statistics and probability theory albeit two appendices have been dedicated to provide a rudimentary discussion.
Table of contents :
Front Matter....Pages i-xvii
Some Basic Remarks....Pages 1-13
Front Matter....Pages 15-15
Numerical Differentiation....Pages 17-28
Numerical Integration....Pages 29-50
The Kepler Problem....Pages 51-59
Ordinary Differential Equations: Initial Value Problems....Pages 61-79
The Double Pendulum....Pages 81-96
Molecular Dynamics....Pages 97-109
Numerics of Ordinary Differential Equations: Boundary Value Problems....Pages 111-122
The One-Dimensional Stationary Heat Equation....Pages 123-129
The One-Dimensional Stationary Schrödinger Equation....Pages 131-146
Partial Differential Equations....Pages 147-168
Front Matter....Pages 169-169
Pseudo Random Number Generators....Pages 171-183
Random Sampling Methods....Pages 185-195
A Brief Introduction to Monte-Carlo Methods....Pages 197-208
The Ising Model....Pages 209-228
Some Basics of Stochastic Processes....Pages 229-250
The Random Walk and Diffusion Theory....Pages 251-273
Markov-Chain Monte Carlo and the Potts Model....Pages 275-286
Data Analysis....Pages 287-297
Stochastic Optimization....Pages 299-314
Back Matter....Pages 315-377

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