The study of knowledge is an important part of knowledge management. In this paper, the mathematical model of knowledge field has been built up in the way of vector field, and the Laplace's equation of knowledge potential has also been built up. This paper takes those examples to explore the solution of mathematical model of knowledge field. It figures out the rules of diffusion of knowledge under the general field circumstances, it aimed at providing a way of quantitative analysis to the diffusion of knowledge, and it combines natural science with social science more effectively.
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