computer game consoles
Many computer games today display some sort of 3D real time graphics. There are two important aspects:
a) the display of a 2D projection of a 3D object model needs involved algorithms that calculate what is visible from the viewpoint of the observer, how objects look like from that perspective and calculate shading and light effects on colors. These algorithms need concepts from 3D geometry (linear algebra, vectors, areas, projection operators etc.). Many computer science departments have classes for the involved mathematics.
b) the animation effects of many games are calculated by numerical solutions of partial differential equations describing the physical motion of solid bodies and fluids. In order to animate fluids like water, for example, computer games use finite element approximations to the Navier-Stokes equations. Needless to say, this is a very active area of current research.
(Computer consoles are actually used in research involving computational fluid dynamics because they are cheap, easy to program and very powerful.)
The last part is also true for automobile design and fabrication:
Car companies need to test new car designs for example for mechanical problems: Are there any parts that will make noise once you drive faster than 50 km/h? This is tested with software that simulates the mechanical parts of the proposed car design using finite element approximations to equations of solid state mechanics. The same technique is also used to simulate crash tests.
The design of the car body is done via CAD (computer aided design) software. This software uses approximation and interpolation algorithms to calculate external surfaces that are as smooth as possible while satisfying boundary conditions that are specified by the designer. These approximations are done e.g. by spline interpolation.
Numerical approximations of computational fluid dynamics are also used to simulate tests in the wind tunnel. This actually saves a lot of money. (It is also the reason why modern cars all kinda look alike.)
