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I am assuming knowledge of Numerical Analysis, and some programming language, including how to use compilers. This is not a programming or C course, though, so students are welcome to use another language of choice.
However, most of the real world cases do not fall in this category, and we need a computer to solve them.
In principle we expect the solutions to qualitatively agree with the intuition gained by solving the simple cases (or "toy models"), but this is not always the case.
Sometimes, the numerical results defy out intuition, and make us reshape our understanding of the problem.
This is the case of "chaos", for instance, where the dynamics of simple classical systems gives rise to some surprising behavior.
I will take some license in the description of some methods, and follow my own notes.
Hopefully class notes will be a good guidance, and the intructor will make an effort to make them available on the course webpage.Therefore, it will also serve as a complementary condensed matter course.The course will be mostly based on this book: Not all topics will be included in the book.This upper-division text provides an unusually broad survey of the topics of modern computational physics from a multidisciplinary, computational science point of view.Its philosophy is rooted in learning by doing (assisted by many model programs), with new scientific materials as well as with the Python programming language.The approach is learning by doing, with model Python programs and Python visualizations for most every topic.(Codes are also available in other computer languages.) The text is designed for a one- or two-semester undergraduate course, or a beginning graduate course. Distinct from the digital version, there is an HTML5 e Text Book version containing additional functionality.The fundamental advantage of using computers in physics is the ability to treat systems that cannot be solved analytically.In the usual situation we can gain insight on the physics of a problem studying soluble models, or limits of a problem that can be treated exactly.The purpose of this course is to introduce students to a series of paradigmatic physical problems in condensed matter, using the computer to solve them.The course will feel like a natural extension of introductory condensed matter, with extra degrees of complexity that make the problems analytically intractable to some extent.