[raj bhatia]

I am talking about an IC. There are myriad fundamental equations but for argument consider the most important feature that makes integration on a large scale possible--lithograpy.. Focusing light through an aperture is fundamental to printing smaller lines on ICs and hence the exponential increase in speed. The problem is fully described by Fourier optics. Solving the diffraction integral for a given boundary condition through an aperture enables you to fully solve the inverse problem--what should the aperture look like to get a required small light spot. This aperture is printed on the mask.

So without the Diffraction integral and determining the spatial components that comes to focus at the focal plane(Fourier Optics), there would be no lithogrpahy. This whole field was characterized to death a 2 centuries ago. The solid theoretical framework enabled large scale integration.

I can go on and on. The work on Noise in Bell labs in the 20's enables proper transistor switching. The heat diffusion equation enables solving for temperature contours across a chip. Quantum mechanics provides the basic framework for carrier transport in devices.

Need more?

[Logophile]

So without the Diffraction integral and determining the spatial components that comes to focus at the focal plane(Fourier Optics), there would be no lithogrpahy. This whole field was characterized to death a 2 centuries ago. The solid theoretical framework enabled large scale integration.

So the theory was fully developed 200 years ago? That was long before the National Science Foundation was created. How did Fourier manage without a government grant?

If you are saying that a sound theoretical foundation is important for developing technology, I will not disagree with you. (Although I would point out that the development of the technology sometimes precedes the development of the theory.) But that does not mean that tax money is required to do theoretical research.