- formulate engineering problems as pdes using calculus and linear algebra
- solve pdes using a calculus and linear algebra boosted by a computer
- determine input data.
onsdag 30 september 2009
Death and Rebirth of the Computing Engineer 3
What would a modern engineering education boosted by computational mathematics look like? Let us see:
Mathematical models of physical systems consist of system of partial differential equations of the form:
(pde) du/dt = f(u,Du,x,t)
where u(x,t) is a given function of a space-time coordinate (x,t) and f(u,Du,x,t) is a function of
(u,Du,x,t) where Du represents derivatives of u with respect to x. The partial differential equation or pde is supposed to hold for x in some domain in space, and t in some interval of time, and the pde is complemented by certain given boundary conditions at the boundary of the domain and a given value of u at initial time. The idea is to determine the function u(x,t) satisfying (pde) for some given data, because the function u(x,t) carries information about the output response of the system to the given input data.
As a basic example: Newton's equations of motion take the form
dX/dt = V, mdV/dt = F(X,V,t)
where X(t) and V(t) denote the position and velocity at time t of a pointlike body of mass m acted upon by a force F. Solving this equation with given initial position and velocity will give
information about these quantities at a later time. Genial! And very useful in enginering design
and control. If you want to direct a rocket to hit Mars for example, you can to that by solving Newton's equations, if you only know where Mars is.
Once you have formulated the pde with given data, you use a computer to compute the solution
using the finite element method. This leads to the following plan for your engineering studies: Learn how to
This will take you about a year, and will bring to the level of present education after 4 years.
The remaining 3 years of a 4 year education, you can spend by digging deeper into
whatever field you may interested in and inventing new devices designed by computation.
What do you say? Would you be interested in such an education if was available?
The proposed program in Simulation Technology at KTH could fill your need. The trouble is that it has not yet started, because traditional program administrators are not enthousiastic about a competing modern program. As a student you can help to balance forces by expressing your interest in the new program.