Notes for PDE I, Spring 2004
نویسنده
چکیده
1.1 Variables The independent variables are x , t : the length along the road and time. The main dependent variables are ρ ,Q : the car density and flux: number of cars per unit length of the road, and number of cars crossing a section per unit time; and U : the mean car velocity. The three dependent variables are related by the identity Q = ρU , (1) which follows from the following considerations. The number of cars crossing a section at speed u in the time interval dt equals the number of cars with that speed in the spatial interval dx = u dt. Hence, for a uniform car speed, (1) follows. To take averages over the various car speeds in the general case, we need to introduce the density in phase space r(x, t, u) , so that ∫ u2
منابع مشابه
PDE from a probability point of view
These notes are for a course I gave while on sabbatical at UBC. It presupposes the reader is familiar with stochastic calculus; see the notes on my web page for Stochastic Calculus, for example. These notes for the most part are based on my book Diffusions and Elliptic Operators, Springer-Verlag, 1997. The topics covered are: stochastic differential equations, solving PDEs using probability, Ha...
متن کاملTopics in Logic and Foundations: Spring 2004
This is a set of lecture notes from a 15-week graduate course at the Penn-sylvania State University taught as Math 574 by Stephen G. Simpson in Spring 2004. The course was intended for students already familiar with the basics of mathematical logic. The course covered some topics which are important in contemporary mathematical logic and foundations but usually omitted from introductory courses...
متن کاملFourth-order numerical solution of a fractional PDE with the nonlinear source term in the electroanalytical chemistry
The aim of this paper is to study the high order difference scheme for the solution of a fractional partial differential equation (PDE) in the electroanalytical chemistry. The space fractional derivative is described in the Riemann-Liouville sense. In the proposed scheme we discretize the space derivative with a fourth-order compact scheme and use the Grunwald- Letnikov discretization of the Ri...
متن کاملCommutative Algebra I
1 A compilation of two sets of notes at the University of Kansas; one in the Spring of 2002 by ?? and the other in the Spring of 2007 by Branden Stone. These notes have been typed
متن کامل