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Latest revision as of 09:16, 27 October 2022
PHYS 460/660: Computational Methods of Physics
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What is Computational Physics?
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Computational physics is physics done by means of computational methods. Computers do not enter into this tentative definition. The essential point in computational physics is not the use of machines, but the systematic application of numerical techniques and algorithms that approximate physical description of complicated systems. The usage of computational methods in place of, or in addition to, analytical methods, renders accessible to mathematical description as large a part of physical reality as possible. A number of fundamental techniques of our craft were introduced by Newton, Gauss, Jacobi, and other pioneers who lived quite some time before the invention of workable calculating machines.
Four Pillars of Computational Methods:
To be sure, nobody in his right state of mind would apply stochastic methods by throwing dice, and the iterative solution of differential equations is feasible only in conjunction with the high computing speed. Nevertheless, computational physics is much more than "Physics Using Computers."
Why is computation becoming so important in physics? One reason is that most of analytical tools, such as differential calculus, are best suited to the analysis of linear problems. However, many natural phenomena are nonlinear and are, therefore, extremely sensitive to small changes in variables. Another incentive to employ computational methods are systems with many degrees of freedom. Moreover, asking questions like "How can I formulate the problem on a computer?" has led to new formulation of scientific laws as rules for a computer rather being expressed in terms of differential equations (thus, viewing computer as a physical systems one can try to develop novel computer architectures that would model physical systems in nature more efficiently).
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News
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- Project 6 is posted and it is due on 05/27 by midnight.
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Lecture in Progress
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- Ex Cathedra: Lecture 7: Interdisciplinary Topics in Complex Systems
- Hands-on Lab: Code development for Project 6.
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Course Motto
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- In teaching, writing, and research, there is no greater clarifier than a well-chosen example.
- Formalism should not be introduced for its own sake, but only when it is needed for some particular problem.
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