Thursday, July 18, 2019

Computational Physics (Free PDF)

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So, ultimately, in order to understand nature it may be necessary to have a deeper understanding of mathematical relationships. But the real reason is that the subject is enjoyable, and although we humans cut nature up in different ways, and we have different courses in different departments, such compartmentalization is really artificial, and we should take our intellectual pleasures where we find them. Richard Feynman, The Laws of Thermodynamics.

Why a preface you may ask? Isn’t that just a mere exposition of a raison d’╦ćetre of an author’s choice of material, preferences, biases, teaching philosophy etc.? To a large extent I can answer in the affirmative to that. A preface ought to be personal. Indeed, what you will see in the various chapters of these notes represents how I perceive computational physics should be taught.

This set of lecture notes serves the scope of presenting to you and train you in an algorithmicapproach to problems in the sciences, represented here by the unity of three disciplines, physics, mathematics and informatics. This trinity outlines the emerging field of computational physics.

Part I: Introduction to programming and numerical methods
1. Introduction
2. Introduction to C++ and Fortran
3. Numerical differentiation and interpolation
4. Non-linear Equations
5. Numerical Integration
Part II: Linear Algebra and Eigenvalues
6. Linear Algebra
7. Eigensystems
Part III: Differential Equations
8. Differential equations
9. Two point boundary value problems
10. Partial Differential Equations
Part IV: Monte Carlo Methods
11. Outline of the Monte Carlo Strategy
12. Random walks and the Metropolis algorithm
13. Monte Carlo Methods in Statistical Physics
14. Quantum Monte Carlo Methods
Part V: Advanced topics
15. Many-body approaches to studies of electronic systems: Hartree-Fock theory and Density Functional
16. Improved Monte Carlo Approaches to Systems of Fermions
17. Bose-Einstein condensation and Diffusion Monte Carlo

Author Details
"Morten Hjorth-Jensen"

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