The Scale Of The Solution Spaces Of DEs

In this dissertation, under the guidance of mathematics mechanization and the instruction of the AC=BD theory put forward by Prof. Zhang Hongqing, by means of symbolic computation software, the solution theory of DEs are discussed, especially the Riquier-Janet theory and the formal theory and their applacations in the problem of the scale of the solution space, specifically, they are applied in the PDEs arising from the fields of elastic mechanics and electric dynamics.Chapter 1 is devoted to investigating the ideas of the mathematics mechanization, computer algebra and the mathematical physics equations mechanization.Chapter 2 investigates AC=BD theory and its application, and the methods of constructing of the operators of C and D are introduced.Chapter 3 introduces the methods to measure the scale of the solution spaces of DEs and their applications.