17_80979_Anterrieu.indd

Real experiments are sometimes missing or highly expensive to implement when teaching modern physics. This is an important issue, especially when the theories are not intuitive. However, with the incorporation of computers into the classroom it has become much easier to illustrate some amazing effects of modern physics that cannot be brought to the attention of students without the aid of numerical simulations. Thanks to the performance of MATLAB langage, as well as to the easiness to code a theoretical problem, the students can really conduct numerical expriments and play with them almost in real time. This computer-based teaching approach is illustrate here with the capabilities to use MATLAB for solving initial values problems of ordinary differential equations encountered in relativistic electrodynamics Ordinary differential equations in Matlab In mathematics, an ordinary differential equation (or ODE) is a relation f that contains one or more derivatives of a dependent variable y with respect to a single independent variable t, usually referred to as time. Many studies have been devoted to the solution of ODEs. In the case where the equation is linear, it can be solved by analytical methods. Unfortunately, most of the interesting ODEs are non-linear and, with a few exceptions, cannot be solved analytically. However, in science and in engineering, a numeric approximation to the solution is often good enough to solve a problem. Numerical integration is that part of numerical analysis which studies the numerical solutions of ODEs with the aid of iterative solvers. MATLAB offers several numerical algorithms to solve a wide variety of ODEs. These solvers are designed to handle only explicit ODEs of the form y = f (t, y), linearly implicit ODEs of the form M(t, y) · y = f (t, y) as well as fully implicit ones of the form f (t, y, y ) = 0. Generall

Rural road surfacing: Gravel/laterite (surface option 3)

Metadata only recordThis document discusses advantages and disadvantages of gravel road surfacing, offers design considerations and suggestions, and gives general guidelines for road construction and maintenance. A list of useful references is also provided