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Verification of Taylor's theorem
- 1 Shanghai University
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Abstract
Multivariate function calculus is an important part of mathematical analysis courses, and most conclusions can be found and generalized in univariate calculus. However, the biggest difficulty in teaching multivariate calculus lies in its abstraction, such as Taylor’s theorem, multiple integral regions drawing, and integral variable transformation. At the same time, ordinary differential equations are also one of the basic courses of the profession, and dynamic systems based on ordinary differential equations have extensive applications in mathematical models of continuity problems and optimal control problems. Software such as Mathematica, Python, Matlab, etc. can solve similar problems. Therefore, this article will use the visualization and computational capabilities of Mathematica to validate important definitions and conclusions in multivariate calculus, and compare the differences among the three software in solving approximate numerical solutions of dynamic systems of ordinary differential equations from different perspectives.
Keywords
Taylor’s theorem for multivariate functions, integral transformations, ordinary differential equations, dynamic systems
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Cite this article
Li,Q. (2024). Verification of Taylor's theorem. Theoretical and Natural Science,43,61-67.
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Volume title: Proceedings of the 3rd International Conference on Computing Innovation and Applied Physics
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