by Michael P. Brenner
Publisher: Harvard University 2010
Number of pages: 250
The goal of this course is to give a modern introduction to mathematical methods for solving hard mathematics problems that arise in the sciences -- physical, biological and social. Our aim therefore is to teach, within a broad suite of examples, how computer simulations and analytical calculations can be effectively combined. In this course, we will begin with problems that are simple polynomial equations and first order differential equations -- and slowly march our way towards the study nonlinear partial differential equations.
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by Eric Ayars - California State University, Chico
Contents: Useful Introductory Python; Python Basics; Basic Numerical Tools; Numpy, Scipy, and MatPlotLib; Ordinary Differential Equations; Chaos; Monte Carlo Techniques; Stochastic Methods; Partial Differential Equations; Linux; Visual Python; etc.
by Johan Hoffman, Claes Johnson
Computational foundation of thermodynamics based on deterministic finite precision computation without resort to statistics. A new 2nd Law without the concept of entropy is proved to be a consequence of the 1st Law and finite precision computation.
by Volker Springel - arXiv
These are lecture notes about high performance computing and numerical modelling in 43rd Saas Fee Advanced Course winter school, specifically covering the basics of numerically treating gravity and hydrodynamics in the context of galaxy evolution.
by T. H. Pulliam - NASA
Implicit finite difference schemes for solving two dimensional and three dimensional Euler and Navier-Stokes equations will be addressed. The methods are demonstrated in fully vectorized codes for a CRAY type architecture.