浅析极限思想地产生与发展9(1).doc

实用标准文案 实用标准文案 精彩文档 精彩文档 石家庄学院毕业论文 PAGE \* MERGEFORMAT 1 毕 业 论 文 毕 业 论 文 题 目： 浅析极限思想的产生与发展 学 院： 数学与信息科学学院 专 业： 数学与应用数学 班 级： 2011级1班 姓 名： 季满 学 号： 20110501005 指导教师： 曹志军 2015 年 5 月 20 日 实用标准文案 精彩文档 浅析极限思想的产生和发展 【摘要】极限思想是一种重要的数学思想，这个理论的完善历经几个世纪。由远古的萌芽时期，到中世纪后随着微积分的创立和应用得到进一步发展，再到18世纪后随着微积分的严密化极限思想达到成熟，形成完善系统的极限理论，这期间布满了众多数学家和哲学家辛勤的汗水和孜孜追求的奋斗足迹。极限思想的发展历程，充分体现了人类探索真理、追求创新的宝贵精神，充分体现了人类认识世界和改造世界的强烈愿望。 极限思想是一种重要的数学思想，是辩证法在数学中的完美体现。本文阐述了对极限思想的辩证理解， 阐述了通过极限这一工具，如何从有限认识了无限，从对事物的近似认识到精确认识，从事物的多样性变化中认识了统一性的变化，在直与曲的对立中认识了统一。 【关键词】极限思想；发展；辩证法；辩证统一 The emergence and development of the limit idea 【Abstract】limit thought is an important mathematical idea. It is formed through a long historical process. It is from ancient infancy to the further development with the creation and application of calculus in the middle ages. It forms a complete system limit theory with the further close of calculus which is after the eighteenth century. The process is filled with many sweats and the struggle footprints of mathematicians and philosophers. The development process of limit thought fully reflects the human search for truth and the precious spirit which is in pursuit of innovation. The development process of limit thought also fully reflects strong desire to understand the word and transform the world. Limit thought is an important mathematical idea. Dialectics is displayed perfectly in the mathematics. The paper describes the dialectical understanding about limit thought. We recognize the infinite from limited thought and the accurate understanding from approximate understanding through the limit thought. We recognize the unity changes from diversity changes and recognize straight and curved unity from the opposition. 【Key Words】limit thought ；development ；dialectics ；dialectical unity